Influence of Laser Intensity Fluctuation on Single-Cesium Atom Trapping

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Article Inﬂuence of Laser Intensity Fluctuation on Single-Cesium Atom Trapping Lifetime in a 1064-nm Microscopic Optical Tweezer

Rui Sun 1, Xin Wang 1, Kong Zhang 1, Jun He 1,2 and Junmin Wang 1,2,* 1 State Key Laboratory of Quantum Optics and Quantum Optics Devices, and Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China; [email protected] (R.S.); [email protected] (X.W.); [email protected] (K.Z.); [email protected] (J.H.) 2 Collaborative Innovation Center of Extreme Optics of the Ministry of Education and Shanxi Province, Shanxi University, Taiyuan 030006, China * Correspondence: [email protected]

Received: 16 December 2019; Accepted: 13 January 2020; Published: 16 January 2020

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Abstract: An optical tweezer composed of a strongly focused single-spatial-mode Gaussian beam of a red-detuned 1064-nm laser can confine a single-cesium (Cs) atom at the strongest point of the light intensity. We can use this for coherent manipulation of single-quantum bits and single-photon sources. The trapping lifetime of the atoms in the optical tweezers is very short due to the impact of the background atoms, the parametric heating of the optical tweezer and the residual thermal motion of the atoms. In this paper, we analyzed the influence of the background pressure, the trap frequency of optical tweezers and the laser intensity fluctuation of optical tweezers on the atomic trapping lifetime. Combined with the external feedback loop based on an acousto-optical modulator (AOM), the intensity fluctuation of the 1064-nm laser in the time domain was suppressed from 3.360% to ± 0.064%, and the suppression bandwidth in the frequency domain reached approximately 33 kHz. ± The trapping lifetime of a single-Cs atom in the microscopic optical tweezers was extended from 4.04 s to 6.34 s.

Keywords: optical tweezer; atomic trapping lifetime; parametric heating; suppression of laser intensity ﬂuctuation

1. Introduction The physical implementation of a single-photon source has important application value in the fundamental research of quantum optics and linear quantum computation, especially the controllable triggered single-photon source as its core quantum source. Generally, one can generate single-photons via single-atom, single-molecule, single-ion, single-quantum dots or parametric down-conversion. Compared with the said ways, single-atoms have advantages of narrowband, matching atom transition lines and weak coupling of neutral ground-state atoms with background light and external electromagnetic fields. Single-atom source based on the captured single-atom in an optical tweezer [1–3] paves the way for quantum repeaters, quantum teleportation, quantum secure communications and linear quantum computing. In 1975, Hansch and Schawlow first put forward the use of the laser to cool neutral atoms [4]. In 1987, the research group led by Steven Chu cooled and captured neutral Sodium atoms with magneto-optical trap (MOT) for the first time [5]. In 1994, Kimble’s team first achieved the cooling and capture of a single-atom [6]. In 2016, the Browaeys group constructed a

Appl. Sci. 2020, 10, 659; doi:10.3390/app10020659 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 659 2 of 11 two-dimensional atom array composed of 50 single-atoms trapped in optical tweezers [7]. In 2018, Browaeys group constructed a three-dimensional atom array composed of 72 single-atoms trapped in optical tweezers, optionally manipulating the spatial position of each atom [8]. In our system, we have already captured [2,9] and transferred [10,11] single-atoms to optical tweezer efficiently, built cesium (Cs) magic-wavelength optical dipole trap [2,3], and finally achieved triggered single-photon source at 852 nm based on single-atom manipulation [3,12]. When manipulating the single-atoms in the optical tweezers, it is required that the atoms be captured. We must capture all the atoms in the tweezers before finishing all the operations. Therefore, it is important to prolong the trapping lifetime of atoms in the optical tweezer, to improve the experimental efficiency and the experimental accuracy. The trapping lifetime of an atom in the optical tweezer is limited by many factors such as recoil heating, laser intensity fluctuation, the degree of atomic vapor, laser beam pointing stability and the residual atom thermal motion. One can suppress the laser intensity fluctuation [13], increase background vacuum degree, improve the laser pointing stability, increase the laser power and adopt the polarization gradient cooling [14] to prolong the trapping lifetime of a single-atom in the optical tweezer. In this work, we discussed the influence of the vacuum degree and the light intensity fluctuation of 1064-nm optical tweezer on atom trapping lifetime and the experimental methods of improving the fluctuation of the laser intensity. Generally, one can suppress the laser intensity fluctuation with optical mode cleaner [15], optical inject lock [16] or acousto-optical modulator (AOM) feedback [13,17]. Thanks to its flexibility and simplified experimental setup, the AOM feedback becomes the best candidate to suppress the laser intensity fluctuation only by controlling the diffraction efficiency of AOM.

2. Single-Atom Magnetic Optical Trap Ideally, the lifetime of single-atom in the optical tweezer is identical to the lifetime of the atom state, which means the lifetime for a ground-state atom can be extremely long. The trapping life of the ground state atoms in the optical tweezers is limited due to the influence of background atoms collision, the parametric heating of the optical tweezers and the residual thermal motion of the atoms. The individual atom trapped in the optical tweezer will collide with the free atoms in the Cs gas chamber. In this process the single-atom gains kinetic energy, heats up and eventually escapes from the optical tweezer, resulting in the reduction of the atomic trapping lifetime. In the experiment, we can reduce the collision probability of induced heating by increasing the background vacuum of the cesium atom gas chamber and reducing the number of background atoms. This can extend the trapping lifetime to some extent. Since the probe of the thermal ionization gauge in the vacuum system is far away from the cesium atom gas chamber, the measured vacuum may be different from the actual vacuum degree in the Cs atomic vapor cell. By measuring the typical time of the MOT, we can know the pressure level in the Cs atomic gas chamber more accurately. In our scheme, due to MOT capturing the atoms in the chamber, it is impossible to isolate trapped atoms from background atoms. Thus, we measure and fit the loading curve instead of using release and recapture to get the typical time of MOT [17]. The background pressure is related to the atomic density N in the vapor cell [18] r 1 M N = (1) τσ 3kBT where τ is the atomic trapping lifetime in the MOT, σ is the atomic collision cross-section of Cs, M is the mass of Cs atom, kB is the Boltzmann constant, according to the pressure formula p = NkBT the pressure (p) in the vapor cell is [18] √3Mk T p = B (2) 3τσ Appl. Sci. 2020, 10, 659 3 of 11

Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 12 Figure1 shows the loading curve of the magneto-optical trap when the cooling laser power of the Figure 1 shows the loading curve of the magneto-optical trap when the cooling laser power of MOT isthe 150 MOTµW, and is 150 the μW, magnetic and the ﬁeld magnetic gradient field is gradient 151.41 Gauss is 151.41/cm. Gauss/cm. For atom For number atom numberN(t = 0) = 0 t/τ as initial condition and ﬁt the curve with N(t) = NS 1 e [18], thet / typical time of the MOT is Nt 00 as initial condition and fit the curve with N− t  NS 1 e  [18], the typical time − 7 5.81 0.14 s, and the pressure in the chamber is about 6 10 Pa. The−7 temperature of atoms in the ± of the MOT is 5.81 ± 0.14 s, and the pressure in the chamber× is −about 6 × 10 Pa. The temperature of MOT isatoms ~105 inµK the under MOT similaris ~105 μ conditionsK under similar [19 conditions]. [19].

2500 Cesium atoms MOT 2250 Loading time constant: 2000 ~ 5.81 ± 0.14 s

1750

1500

1250

1000

750

(counts in 50 ms time bin) time ms 50 in (counts Pressure: ~ 6x10^(-7) Pa; 500 Cooling beam@852 nm: ~150 W;

Fluorenscence photon counting signal signal counting photon Fluorenscence 250 Repum beam@894 nm: ~ 50 W; Magnetic gradient: 151.41 Gauss/cm 0 0 2 4 6 8 10 12 14 16 18 20 22 MOT loading time (s) Figure 1.FigureLoading 1. Loading curve curve of the of the magneto-optical magneto-optical traptrap (MOT). The The MOT MOT is empty is empty when when the quadrupole the quadrupole magneticmagnetic field is field turned is turned off. off. After After the the quadrupole quadrupole magnetic field field is turned is turned on, atoms on, atoms are gradually are gradually loaded into the MOT. The typical time constant of the MOT is 5.81 ± 0.14 s, and the corresponding loaded into the MOT. The typical time constant of the MOT is 5.81 0.14 s, and the corresponding pressure in the Cs vapor cell is approximately 6 × 10−7 Pa. ± pressure in the Cs vapor cell is approximately 6 10 7 Pa. × − Adjusting the spatial overlap and temporal overlap of the MOT and the optical tweezer can Adjusting the spatial overlap and temporal overlap of the MOT and the optical tweezer can transfer the single-atom between the traps efficiently. The loading rate of the MOT RL is sensitive transfer the single-atom between the traps efficiently. The loading rate of the MOT14R is sensitive to the dB dB 3 L to the axial gradient of the quadrupole magnetic field , and 14 [19,20]. The dB  dB −3 RL   axial gradient of the quadrupole magnetic field , and RdzL [19,20dz]. The smaller the axial dz ∝ dz gradientsmaller of the the quadrupole axial gradient magnetic of the quadrupole field, the magnetic higher field, the MOTthe higher loading the MOT rate loa andding the rate more and the captured atoms. Conversely,more captured theatoms. higher Conversely, the magnetic the higher field the magnetic gradient, field the gradient, lower the lower MOT the loading MOT loading rate and the rate and the fewer atoms trapped. fewer atoms trapped. Since the loading rate of the MOT is pretty sensitive to the axial gradient of quadrupole magnetic Sincefield, the we loading can use ratea trigger of the loop MOT to control is pretty the sensitiveloading rete to of the the axial MOT gradient automatically. of quadrupole As shown in magnetic field, weFigure can 2a, use the a fluorescent trigger loop photons to control are collected the into loading the single rete-photon of the counting MOT automatically. module (SPCM), and As shown in Figurethe2a, output the fluorescent pulses of SPCM photons enter the are pulse collected counter. into Then the we single-photon can set the output counting voltage of module the pulse (SPCM), and thecounter output for pulses different of SPCM circumstances enter the that pulse represents counter. the atom Then numbers we can in set the the MOT. output The output voltage voltage of the pulse counterof for the di pulsefferent counter circumstances enters the quadrupole that represents magnetic the field atom power numbers supply in (Model the MOT. SM 70 The-22, outputDELTA, voltage Holland) as control voltage. The output current of the power supply will change related to the control of the pulse counter enters the quadrupole magnetic field power supply (Model SM 70-22, DELTA, voltage, and the quadrupole magnetic field gradient and the loading rate of the MOT change, too. Holland) asFigure control 2(b voltage.) and Table The 1 shows output the current working of principle the power of the supply trigger willloop. change When the relatedre is only to theone control voltage,atom and in the the quadrupole MOT, the output magnetic voltage field of the gradient pulse counter and the keeps loading at 3.8 V, rate the of quadrupole the MOT magnetic change, too. Figurefield2 gradientb and Table stays 1at shows 232 Gauss/cm. the working When there principle is no atom of the in triggerthe MOT, loop. the output When voltage there of is the only one atom inpulse the MOT,counter the varies output between voltage 1.50 V of 1.79 the V pulseand let counterthe loading keeps rate of at the 3.8 MOT V, the goes quadrupole up. Under this magnetic circumstance, the output current of the power supply goes down automatically and the quadrupole field gradient stays at 232 Gauss/cm. When there is no atom in the MOT, the output voltage of the magnetic field gradient change between 103 Gauss/cm and 116 Gauss/cm. For multi-atom condition, pulse counterthe output varies voltage between of the 1.50pulseV counter 1.79 V rises, and and let thethe loading rate rate of of the the MOT MOT descends. goes up. On Underthis this circumstance,occasion, the the output output current of of the the power power supply supply rises goesand the down quadrupole automatically magnetic and field the gradient quadrupole magneticchanges field gradientbetween 273 change Gauss/cm between and 316 103 Gauss/cm, Gauss/ cmand andthe atom 116 number Gauss/ cm.in the For MOT multi-atom cuts down. condition, the output voltage of the pulse counter rises, and the loading rate of the MOT descends. On this occasion, the output current of the power supply rises and the quadrupole magnetic field gradient changes between 273 Gauss/cm and 316 Gauss/cm, and the atom number in the MOT cuts down. Figure3 shows the probability of the single-atom in the MOT in the cases of trigger loop o ff or on respectively. The power of the 852-nm MOT cooling laser is 150 µW, and the power of the 894-nm repumping laser is 50 µW. When the trigger loop is off, the loading rate of the single-atom is merely 28.4%, and the 2 atoms loading rate reaches up to 56.8%. The loading rate of single-atom rises to 80.2% when the trigger loop is on, and the multi-atom rate declines sharply. Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 12

1600 quadrupole magnetic field (b) gradient 294 Gauss/cm 3 atoms ) 1400 quadrupole magnetic field 1374 counts 1200 gradient 283 Gauss/cm

1000 2 atoms 943 counts Appl. Sci.Appl.2020 Sci., 10 20, 65920, 10, x FOR PEER REVIEW 800 4 of 12 4 of 11 quadrupole magnetic field 600 gradient 232 Gauss/cm 1 atom

(counts/ 50 ms time bin) time ms 50 (counts/ 530 counts 400 quadrupole magnetic field Fluorenscence photon counting signals counting photon Fluorenscence 200 1600 gradient110quadrupole Gauss/cm magnetic field0 atom 0 (b) gradient 294 Gauss/cm 82 counts 3 atoms ) 14000 5 10 15 20 1374 counts quadrupole magneticTime field (s) 1200 gradient 283 Gauss/cm

1000 2 atoms Figure 2. Single-atom loading trigger loop. (a) Pulse counter adjusts the output voltage according943 counts to 800 different photon counts. We use the output analog voltage to control thequadrupole output magnetic current field of power 600 gradient 232 Gauss/cm 1 atom

supply and the quadrupole magnetic field gradient.bin) time ms 50 (counts/ Keys to (a) single-photon counting module530 counts 400 (SPCM); insulated gate bipolar transistor (IGBT); (b) The trigger loop dynamicallyquadrupole magnetic changes field the Fluorenscence photon counting signals counting photon Fluorenscence 200 loading rate of atoms in the MOT by adjusting the quadrupole magnetic field gradient110gradient. Gauss/cm 0 atom 0 82 counts 0 5 10 15 20 Table 1. Pulse counter and power supply parameter setting.Time (s)

FigureFigure 2. Single-atom 2. Single-atom loading loading trigger triggerPulse loop.loop. Counter (a ()a Pulse) Pulse counter counter adjusts adjusts the output theQuadrupole outputvoltage according voltage Magnetic accordingto Atom Photon Counts Power Supply Analog Output Field Gradient to diNumbersfferentdifferent photon photon(Counts/50 counts. counts. ms) We We useuse thethe output analog analog voltageOutput voltage to Current control to control (A)the output the output current current of power of power supplysupply and the and quadrupole the quadrupole magnetic magnetic fieldVoltage fieldgradient. (V) gradient. Keys Keys to (a) to single-photon (a) single-photon counting counting(Gauss/cm) module module (SPCM); Lower Upper Lower Upper Lower Upper Lower Upper insulated(SPCM);- gate bipolar insulated transistor gate bipolar (IGBT); transistor (b) The (IGBT); trigger (b) The loop trigger dynamically loop dynamically changes changesthe loading the rate of loading rateBound of atoms inBound the MOT Bound by adjusting Bound the quadrupoleBound magneticBound field gradient.Bound Bound atoms in0 the MOT by0 adjusting499 the quadrupole1.50 1.79 magnetic 7.0 field gradient.7.9 103 116 1 500 Table600 1. Pulse3.80 counter and3.80 power supply17.3 parameter17.3 setting. 232 232 2 601Table 1.1500Pulse counter4.00 and4.50 power supply18.6 parameter20.7 setting.273 304 3 1501 2500 4.51Pulse Counter4.70 20.8 21.5 Quadrupole306 Magnetic316 AtomAtom PhotonPhoton Counts Counts Pulse Counter Analog Output PowerPower Supply Supply Quadrupole Magnetic Field Analog Output Field Gradient NumbersNumbers (Counts(Counts/50/50 ms) ms) Voltage (V) OutputOutput Current Current (A)(A) Gradient (Gauss/cm) Voltage (V) (Gauss/cm) Figure 3 showsLower the UpperprobabilityLower of the singleUpper-atom in theLower MOT Upperin the casesLower of trigger loopUpper off or - BoundLower BoundUpper BoundLower UpperBound LowerBound UpperBound BoundLower BoundUpper on respectively.- The power of the 852-nm MOT cooling laser is 150 μW, and the power of the 894-nm Bound Bound Bound Bound Bound Bound Bound Bound repumping0 laser 0is 50 μW. 499 When the 1.50 trigger loop 1.79 is off, the 7.0loading rate 7.9 of the single 103-atom is 116 merely 0 0 499 1.50 1.79 7.0 7.9 103 116 28.4%, and1 the 2 500 atoms loading 600 rate 3.80 reaches up 3.80 to 56.8%. 17.3The loading 17.3 rate of 232single-atom 232 rises to 1 500 600 3.80 3.80 17.3 17.3 232 232 80.2% when2 the 601trigger loop 1500 is on, and 4.00 the multi- 4.50atom rate declines 18.6 sharply. 20.7 273 304 32 1501601 25001500 4.514.00 4.50 4.70 18.6 20.8 20.7 21.5 306273 316304 3 1501 2500 4.51 4.70 20.8 21.5 306 316

30 Figure1400 3 shows the probability of the single-atom in the MOT in the cases of trigger loop off or trigger off (b) 1 atom on respectively.1200 (a) The power of the 852-nm MOT cooling laser25 is 150 μW,28.4 and % the power of the 894-nm 2 atoms repumping1000 laser is 50 μW. When the trigger3 atomsloop is off, the loading rate of the single-atom is merely 20 56.8 % 28.4%, and the 2 atoms loading rate reaches957 countsup to 56.8%. The loading rate of single-atom rises to 800 2 atoms 80.2% when the trigger loop is on, and the multi660 counts-atom rate15 declines sharply.

Occurs 0 atom 600 5.7 % 1 atom (counts/ 50 ms time bin) time ms 50 (counts/ 400 10 425 counts 3 atoms 30 9.1 %

Fluorenscencesignals counting photon 200 1400 5 trigger off 0 atom 1 atom 0 81 counts (b) 1200 (a) 25 28.4 % Appl. Sci. 2020, 010, x FOR50 PEER100 REVIEW150 200 250 300 0 5 of 12 Time (s) 0 200 400 600 2 800atoms 1000 1200 1400 1000 3 atoms 20 Fluorenscence photon 56.8counting % signals 957 counts (counts/ 50 ms time bin) 800 2 atoms 15 800 660 counts 80

Occurs 0 atom 600 trigger on (d)5.7 % 700 (c) 1 atom 70 1 atom

(counts/ 50 ms time bin) time ms 50 (counts/ 10 400 80.2 % 4252 atoms counts 3 atoms 600 607 counts 60 9.1 % Fluorenscencesignals counting photon 200 5 500 0 atom 50 0 81 counts 400 0 50 100 150 200 250 300 0 atom Occurs 400 1 atom Time (s) 0 10.2200 % 400 600 800 1000 1200 1400 300 360 counts 30 Fluorenscence photon counting signals

(counts/ 50 ms time bin) time ms 50 (counts/ (counts/ 50 ms time bin) 200 20 2 atoms

Fluorenscence photon counting signals counting photon Fluorenscence 100 9.6 % 0 atom 10 0 59 counts 0 0 50 100 150 200 250 300 Time (s) 0 100 200 300 400 500 600 700 800 Fluorenscence photon counting signals (counts/ 50 ms time bin)

FigureFigure 3. The 3. loadingThe loading probability probability of of single-atom single-atom in in the the MOT. MOT. The The trigger trigger loop canloop suppress can suppress the the probabilityprobability of multi-atom of multi-atom in in the the MOT MOT andand improve improve the the probability probability of single of single-atom.-atom. (a) and (b (a) ,Whenb) When the triggerthe loop trigg turneder loop oﬀ turned, the loading off, the probabilityloading probability of single-atom of single-atom in the in MOT the MOT within within 300 300 s is s only is only 28.4%, and the probability28.4%, and of the multiple-atom probability of multiple and zero-atom-atom and is zero as high-atom as is 71.6%,as high as which 71.6%, is which obviously is obviously not conducive not to conducive to the measurement in subsequent experiments. (c) and (d) For the trigger loop on, the the measurement in subsequent experiments. (c,d) For the trigger loop on, the probability of single-atom probability of single-atom in the MOT increases to 80.2%, while the probability of multi-atom loading in the MOT increases to 80.2%, while the probability of multi-atom loading is signiﬁcantly suppressed. is significantly suppressed.

We can see in Figure 3 that there is still certain photon-counting while there is no atom in the MOT. This is partly because the cooling and repumping laser hits the glass cell wall with scattering and reflecting, the scattered photons at certain specific angles will enter the fluorescence collection system. Moreover, the background atoms move to the MOT laser path will interact with laser and emitted fluorescent photons enter the fluorescence collection system, resulting in the generation of the background photon counting. Besides, since the experimental conditions such as MOT cooling laser power and ambient temperature cannot be the same in each experiment, the background photon count in the MOT cannot be completely consistent but varies within a certain range.

3. Parametric Heating of Atoms in an Optical Tweezer Atoms in optical tweezers will generate electric dipole moments under the action of the oscillating electric field. We can regard these atoms as electric dipoles interacting with the oscillating external field. As shown in Figure 4 (a) when the electric dipole is driven by an electric field with a frequency lower than the resonant frequency of atomic transition, due to the effect of attraction, the atom will be captured in the region with the strongest electric field. Otherwise, when the electric dipole is driven by an electric field with a frequency higher than the resonant frequency, the atom will be excluded from the region with the strongest electric field. In other words, when the frequency of optical tweezer is red-detuning to the atomic transition frequency concerned, the atoms are captured at the bottom of the optical tweezer [21]. When the optical tweezer frequency is blue- detuning to the atomic transition frequency, the atoms will be excluded from the optical tweezer [22]. Using a focused single-spatial-mode Gaussian beam with red detuning can form an optical tweezer [23], with intensity distribution in the axial and radial direction as follows, 2Pr2 I( r , z )=22 exp 2 (3)  w()() z w z

where P is the power of the optical tweezer laser and wz() is the beam radius at z [23],

z2 w( z ) w0 1 2 (4) zR Appl. Sci. 2020, 10, 659 5 of 11

We can see in Figure3 that there is still certain photon-counting while there is no atom in the MOT. This is partly because the cooling and repumping laser hits the glass cell wall with scattering and reflecting, the scattered photons at certain specific angles will enter the fluorescence collection system. Moreover, the background atoms move to the MOT laser path will interact with laser and emitted fluorescent photons enter the fluorescence collection system, resulting in the generation of the background photon counting. Besides, since the experimental conditions such as MOT cooling laser power and ambient temperature cannot be the same in each experiment, the background photon count in the MOT cannot be completely consistent but varies within a certain range.

3. Parametric Heating of Atoms in an Optical Tweezer Atoms in optical tweezers will generate electric dipole moments under the action of the oscillating electric field. We can regard these atoms as electric dipoles interacting with the oscillating external field. As shown in Figure4a when the electric dipole is driven by an electric field with a frequency lower than the resonant frequency of atomic transition, due to the effect of attraction, the atom will be captured in the region with the strongest electric field. Otherwise, when the electric dipole is driven by an electric field with a frequency higher than the resonant frequency, the atom will be excluded from the region with the strongest electric field. In other words, when the frequency of optical tweezer is red-detuning to the atomic transition frequency concerned, the atoms are captured at the bottom of the opticalAppl. Sci. tweezer2020, 10, x [FOR21]. PEER When REVIEW the optical tweezer frequency is blue-detuning to the atomic transition7 of 12 frequency, the atoms will be excluded from the optical tweezer [22].

50 (b) w ~ 2.2 ± 0.4 μm ZR ~ 11.7 μm 40 2

Mz ~ 1.18 ± 0.21 (μm)

w 30

20 Beam waist,

0 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 Axial position, z (mm)

Figure 4. Scheme of optical tweezer. (a) A strongly focused single-spatial mode Gaussian beam of aFigure red-detuned 4. Scheme laser of canoptical conﬁne tweezer. atoms. (a) (Ab )strongly The beam focused waist single radius-spatial and Rayleigh mode Gaussian length of beam 1064-nm of a opticalred-detuned tweezer laser are can 2.2 µ confinem and 11.7 atoms.µm, (b respectively.) The beam waist radius and Rayleigh length of 1064-nm optical tweezer are 2.2 μm and 11.7 μm, respectively. Using a focused single-spatial-mode Gaussian beam with red detuning can form an optical tweezerAs shown [23], with in Figure intensity 5, distributionthe part in the in theblue axial box and is used radial to direction measuring as follows,the trap frequency of the optical tweezer, which is an important parameter of the" optical tweezer.# We use a function generator 2P r2 (Model DG635 SRS, America) to loadI(r ,modulationz) = signalsexp 2of different frequencies on AOM 2 (Model(3) 2 2 3110-197, Crystal Technology, America) to simulateπw (z) the intensity− w (z) fluctuation of the optical tweezer so that the optical tweezer will run with intensity fluctuation at a specific frequency. where P is the power of the optical tweezer laser and w(z) is the beam radius at z [23], s z2 w(z) = w 1 + (4) 0 2 zR

q 2U for w0 is the beam wrist, zR is the Rayleigh length, the axial and radial trap frequencies are ωa = 2 MzR q 4U and ωr = 2 , and U is the trap potential depth of the optical tweezer. Mw0

Figure 5. Experimental setup. Polarization-maintaining (PM) fiber; Multi-mode (MM) fiber; magneto- optical trap (MOT); optical-dipole trap (ODT), otherwise the optical tweezer; optical isolator (OI); acousto-optical modulator (AOM); polarization beam splitter (PBS); single-photon counting module (SPCM); ultra-high vacuum (UHV). The red dash box shows the laser intensity fluctuation feedback loop by controlling the diffraction efficiency of AOM 1 to stabilize the intensity fluctuation of the 1064-nm laser. The blue dash box shows the measurement setup of the trap frequency of optical tweezer. The green dash box shows the single-atom cooling and trapping system, the anti-Helmholtz coils, but the cooling and repumping laser beams of the MOT are not shown here.

Then, by measuring the transfer efficiency of single-atom between the MOT and the optical tweezer to observe how the intensity fluctuation of different frequency acts on single-atom trapping lifetime and Figure 6 shows a typical atomic transfer signal between the MOT and the optical tweezer. As shown in Figure 6, the transfer efficiency gets extremely low when the modulation frequency is resonant with the trap frequency and its double frequency of the optical tweezer. Appl. Sci. 2020, 10, 659 6 of 11

The Hamiltonian of single-atom in the optical tweezer is [23]

p2 1 H = + Mω2 [1 + ε(t)]x2, (5) 2M 2 tr

2 for M is the mass of the Cs atom, ωtr = k0/M is the mean square of trap frequency, the elastic coefficient k0 is in direct proportion to the light intensity of optical tweezer I0, we can write the light intensity I(t) I fluctuation as ε(t) = − 0 . Here we use the first-order perturbation theory to clarify how the light I0 intensity fluctuation acts on the single-atom, and take the heating process as the transformation of the atom from n at t = 0 to m , n at t = T. The average transition probability Rm n can express as the | i | i ← power spectral density of the laser intensity fluctuation Sε(ω) [23] Z Z ∞ ∞ D 2 E 2 dωSε(ω) = dυSε(υ) = ε (t) = ε0, (6) 0 0 for ε0 is the mean square of intensity fluctuation and ω = 2πν. The average heating rate of atom in the optical tweezer is [23]

. X D E 2 2 E = P(n)2}ωtr(Rn+2 n Rn 2 n) = ωtrSε(2ωtr) E , (7) ← − ← n − π h i D . E where P(n, t) is the probability of the atom stay at n . For E = Γε E , the constant [23] | i h i

1 2 2 Γε = = π νtrSε(2νtr) (8) TI(sec)

Among others, νtr is the trap frequency. According to Equation (8), the heating rate of single-atom in the optical tweezer is related to the trap frequency and its double frequency of the optical tweezer. For a single-atom in the optical tweezer, it will not only couple with the fluctuation resonance to the trap frequency of the tweezer, but also couple with the double-frequency more intensely. Ultimately, this heating mechanism makes the atom escape from the optical tweezer. We call the process of converting the energy of the double frequency trap into the energy of the fundamental frequency trap as the parametric process. The heating effect of the intensity fluctuation of the laser on the single-atom in the optical tweezer is the process of parametric heating.

4. Measurement of Trap Frequency of Optical Tweezer The output power of the 1064-nm laser (DBR-1064P, Thorlabs, America) and Ytterbium-doped fiber amplifier (YDFA) system is up to 2 W. The output 1064-nm laser beam passes a lens focal length of 100 mm to form a parallel beam with a diameter of 18–19 mm. Then the parallel beam goes through a lens assembly with a focal length of 36 mm and a numerical aperture of NA = 0.29 to form the optical 2 tweezers. Figure4b shows the measurement of the beam waist radius and Mz factor of 1064 nm optical tweezer are 2.2 0.4 µm and 1.18 0.21, respectively. The Rayleigh length Z is 11.7 µm. ± ± R As shown in Figure5, the part in the blue box is used to measuring the trap frequency of the optical tweezer, which is an important parameter of the optical tweezer. We use a function generator (Model DG635 SRS, America) to load modulation signals of different frequencies on AOM 2 (Model 3110-197, Crystal Technology, America) to simulate the intensity fluctuation of the optical tweezer so that the optical tweezer will run with intensity fluctuation at a specific frequency. Then, by measuring the transfer efficiency of single-atom between the MOT and the optical tweezer to observe how the intensity fluctuation of different frequency acts on single-atom trapping lifetime and Figure6 shows a typical atomic transfer signal between the MOT and the optical tweezer. As shown in Figure6, the transfer e fficiency gets extremely low when the modulation frequency is resonant with the trap frequency and its double frequency of the optical tweezer. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 12

50 (b) w ~ 2.2 ± 0.4 μm ZR ~ 11.7 μm 40 2

Mz ~ 1.18 ± 0.21 (μm)

w 30

20 Beam waist,

0 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 Axial position, z (mm)

Figure 4. Scheme of optical tweezer. (a) A strongly focused single-spatial mode Gaussian beam of a red-detuned laser can confine atoms. (b) The beam waist radius and Rayleigh length of 1064-nm optical tweezer are 2.2 μm and 11.7 μm, respectively.

As shown in Figure 5, the part in the blue box is used to measuring the trap frequency of the optical tweezer, which is an important parameter of the optical tweezer. We use a function generator (Model DG635 SRS, America) to load modulation signals of different frequencies on AOM 2 (Model Appl. Sci. 2020, 10, 659 7 of 11 3110-197, Crystal Technology, America) to simulate the intensity fluctuation of the optical tweezer so that the optical tweezer will run with intensity fluctuation at a specific frequency.

FigureFigure 5. 5.ExperimentalExperimental setup. setup. Polarization Polarization-maintaining-maintaining (PM) fiber; (PM) Multi fiber;-mode Multi-mode (MM) fiber; (MM) magneto fiber;- opticalmagneto-optical trap (MOT); trap optical (MOT);-dipole optical-dipole trap (ODT trap), otherwise (ODT), otherwise the optical the tweezer optical tweezer;; optical opticalisolator isolator (OI); acousto(OI); acousto-optical-optical modulator modulator (AOM); (AOM);polarization polarization beam splitter beam (PBS); splitter single (PBS);-photon single-photon counting countingmodule (SPCM);module ultra (SPCM);-high ultra-highvacuum (UHV). vacuum The (UHV). red dash The box red shows dashbox the showslaser intensity the laser fluctuation intensityfluctuation feedback loopfeedback by controlling loop by controlling the diffraction the di ffefficiencyraction e ffiofciency AOM of 1 AOMto stabilize 1 to stabilize the intensity the intensity fluctuation fluctuation of the of 1064the- 1064-nmnm laser. laser. The Theblue bluedash dash box box shows shows the the measurement measurement setup setup of ofthe the trap trap frequency frequency of of optical optical tweezer.tweezer. The The green green dash dash box box shows shows the the single single-atom-atom cooling cooling and and trapping trapping system, system, the the anti anti-Helmholtz-Helmholtz Appl.coil Sci.coils,s ,20 but20 but, the10 the, xcooling FOR cooling PEER and and REVIEW repumping repumping laser laser beams beams of of the the MOT MOT are are not not shown shown here. here. 8 of 12

800 Then, by measuring the transferSingle efficiencyCs atom is transferred of single between-atom MOT and between Tweezer the MOT and the optical 700 tweezer to observe how the intensityDT fluctuationMOT~4.5s,DT ofTweeze differentr~1.0 s. Overlap: frequ 25ency ms. acts on single-atom trapping lifetime and Figure 6 shows a typical600 atomic transfer signal between the MOT and the optical tweezer. As shown in Figure 6, the transfer efficiency gets450 extremely counts/50 ms low when the modulation frequency is 500 resonant with the trap frequency and its double frequency of the optical tweezer. 400

300

200 (counts/ 50 ms time bin) time ms 50 (counts/

100

Fluorenscencesignals counting photon 116 counts/50 ms 0 0 10 20 30 40 50 Time(s) Figure 6.6. AtomicAtomic transfertransfer signal signal between between the the MOT MOT and and the opticalthe optical tweezer. tweezer. The periodThe period is 5.5 s,is in5.5 which s, in thewhich MOT the duration MOT duration is 4.5 s is and 4.5 the s and optical the tweezeroptical tweezer last for last 1.0 s.for The 1.0 MOTs. The overlaps MOT overlaps with the with optical the tweezeroptical tweezer for 25 ms, for and 25 the ms, single-atom and the single is transferred-atom is betweentransferred the between MOT and the the MOT optical and tweezer. the optical tweezer. Figure7 shows the trap frequency and its double frequency on the axial and radial direction. The powerFigure of 7 1064 shows nm the optical trap tweezer frequency is 48.5 and mW, its thedouble optical frequency tweezer trapon the depth axial is 1.3and mK. radial The measureddirection. axialThe power trap frequency of 1064 nm is 4.70 optical kHz, twe for doubleezer is frequency48.5 mW, isthe 9.00 optical kHz (shouldtweezer betrap 9.40 depth kHz), is the 1.3 radial mK. trapThe frequencymeasured axial is 41.80 trap kHz, frequency and the is double 4.70 kHz, frequency for double is 80.80 frequency kHz (should is 9.00 kHz be 83.60 (should kHz). be The9.40 deviationkHz), the betweenradial trap the frequency experimental is 41.80 value kHz, and and the the theoretical double frequency calculation is is 80.80 mainly kHz because (should that be the83.60 suppression kHz). The edeviationﬀect of the between laser intensity the experimental ﬂuctuation value feedback and loopthe theoretical cannot be calculation kept at the sameis mainly level because due to thethat long the durationsuppression of the effect experimental of the laser process. intensity fluctuation feedback loop cannot be kept at the same level due to the long duration of the experimental process.

100 Single Cs atom is transferred between Tweezer and MOT 90

30 Transferring efficiency(%) Transferring 20 41.80±0.09 kHz 9.00±0.06 kHz 10 80.80±0.08 kHz 4.70±0.08 kHz 0 0 20 40 60 80 100 Tweezer intensity dithering frequency(kHz)

Figure 7. Trap frequency and double frequency of the 1064-nm optical tweezer. Transfer efficiency goes an apparent decline when the modulation frequency is resonant or near-resonant to the trap frequency and its double frequency of the optical tweezer and reaches a minimum at resonance.

The photon scattering rate of the optical tweezer is [24]

2 23 3c L  SC =,6 2 2 2 2 (9) 2 0  0 LL  0 

where  is the spontaneous decay rate of the atomic transition, 0 is the transition frequency, L

is the frequency of the optical tweezer. In a 1064-nm optical tweezer, for Cs 6 S1/2 (Fg = 4) −6 P3/2 (Fe = 5) transition, the photon scattering rate is 8.3 photons/s. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 12

800 Single Cs atom is transferred between MOT and Tweezer 700 DTMOT~4.5s,DTTweezer~1.0 s. Overlap: 25 ms.

600 450 counts/50 ms 500

400

300

200 (counts/ 50 ms time bin) time ms 50 (counts/

100

Fluorenscencesignals counting photon 116 counts/50 ms 0 0 10 20 30 40 50 Time(s) Figure 6. Atomic transfer signal between the MOT and the optical tweezer. The period is 5.5 s, in which the MOT duration is 4.5 s and the optical tweezer last for 1.0 s. The MOT overlaps with the optical tweezer for 25 ms, and the single-atom is transferred between the MOT and the optical tweezer.

Figure 7 shows the trap frequency and its double frequency on the axial and radial direction. The power of 1064 nm optical tweezer is 48.5 mW, the optical tweezer trap depth is 1.3 mK. The measured axial trap frequency is 4.70 kHz, for double frequency is 9.00 kHz (should be 9.40 kHz), the radial trap frequency is 41.80 kHz, and the double frequency is 80.80 kHz (should be 83.60 kHz). The deviation between the experimental value and the theoretical calculation is mainly because that the suppression effect of the laser intensity fluctuation feedback loop cannot be kept at the same level Appl.due Sci.to the2020 ,long10, 659 duration of the experimental process. 8 of 11

100 Single Cs atom is transferred between Tweezer and MOT 90

30 Transferring efficiency(%) Transferring 20 41.80±0.09 kHz 9.00±0.06 kHz 10 80.80±0.08 kHz 4.70±0.08 kHz 0 0 20 40 60 80 100 Tweezer intensity dithering frequency(kHz)

Figure 7. Trap frequency and double frequency of the 1064-nm optical tweezer. Transfer eﬃciency goes Figure 7. Trap frequency and double frequency of the 1064-nm optical tweezer. Transfer efficiency an apparent decline when the modulation frequency is resonant or near-resonant to the trap frequency goes an apparent decline when the modulation frequency is resonant or near-resonant to the trap and its double frequency of the optical tweezer and reaches a minimum at resonance. frequency and its double frequency of the optical tweezer and reaches a minimum at resonance. The photon scattering rate of the optical tweezer is [24] The photon scattering rate of the optical tweezer is [24]  2 2 3 2 3πc 23ω  Γ Γ  Γ = 3c L +  , (9) SC =,6 L  2 2 2 + 2  (9) SC 2}ω06ω0 2ωL 2ω0 2ωL 2 2 0  0− LL  0  where Γ is the spontaneous decay rate of the atomic transition, ω0 is the transition frequency, ωL is the where  is the spontaneous decay rate of the atomic transition, 0 is the transition frequency, L frequency of the optical tweezer. In a 1064-nm optical tweezer, for Cs 6 S (Fg = 4) 6 P (Fe = 5) 1/2 − 3/2 transition,is the frequency the photon of the scattering optical tweezer. rate is 8.3 In photonsa 1064-nm/s. optical tweezer, for Cs 6 S1/2 (Fg = 4) −6 P3/2 (Fe = 5) transition, the photon scattering rate is 8.3 photons/s. 5. The Suppression of Laser Intensity Fluctuation

5.1. Experimental Principles and Devices Figure5 shows the scheme of the laser intensity fluctuation control system. The part in the green box is the single-atom capturing and observing system. The optical fiber output beam goes through the collimating lens and expended to a near-parallel beam with a beam diameter of 19 mm. Then the parallel beam passing through the focusing lens assembly (NA = 0.29), and become a tightly focused Gaussian beam with a beam wrist of 2.2 µm. We use the same lens assembly to collect the fluorescence photons of Cs atoms and transfer them into the SPCM through an optical fiber. The part in the red box is the laser intensity fluctuation feedback loop. The first-order diffraction light of AOM 1 as the optical tweezer laser, the zero-order diffraction light as the “energy storehouse” of the first-order diffraction light. The first-order diffraction beam goes through the PBS, the transmission light as the sampling laser, and collected into the detector (New Focus 2051), and the laser intensity fluctuation reflected as the detector’s output voltage. Then the output voltage signal enters the Proportion Integration Differentiation (PID) (Model SIM960, SRS, America) as the reference signal and set feedback-signal-related parameters (e.g., integral time, etc.) of the PID. Next, load the feedback signal on the driving voltage of AOM 1, we can control the diffraction efficiency of AOM 1 precisely. When the optical tweezer laser (the first-order of the diffracted light of AOM 1) intensity decreases (or increases), the output voltage of the sampling detector decreases (or increases) too. The PID output positive feedback (or negative feedback) signal will make the diffraction efficiency of AOM 1increases (or decreases), which means the power of the first-order diffraction light goes up (or down), and of zero-order diffraction light goes down (or up). Finally, we can achieve the purpose of suppressing the fluctuation of laser intensity. Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 12

5. The Suppression of Laser Intensity Fluctuation

5.1. Experimental Principles and Devices Figure 5 shows the scheme of the laser intensity fluctuation control system. The part in the green box is the single-atom capturing and observing system. The optical fiber output beam goes through the collimating lens and expended to a near-parallel beam with a beam diameter of 19 mm. Then the parallel beam passing through the focusing lens assembly (NA = 0.29), and become a tightly focused Gaussian beam with a beam wrist of 2.2 μm. We use the same lens assembly to collect the fluorescence photons of Cs atoms and transfer them into the SPCM through an optical fiber. The part in the red box is the laser intensity fluctuation feedback loop. The first-order diffraction light of AOM 1 as the optical tweezer laser, the zero-order diffraction light as the “energy storehouse” of the first-order diffraction light. The first-order diffraction beam goes through the PBS, the transmission light as the sampling laser, and collected into the detector (New Focus 2051), and the laser intensity fluctuation reflected as the detector’s output voltage. Then the output voltage signal enters the Proportion Integration Differentiation (PID) (Model SIM960, SRS, America) as the reference signal and set feedback-signal-related parameters (e.g., integral time, etc.) of the PID. Next, load the feedback signal on the driving voltage of AOM 1, we can control the diffraction efficiency of AOM 1 precisely. When the optical tweezer laser (the first-order of the diffracted light of AOM 1) intensity decreases (or increases), the output voltage of the sampling detector decreases (or increases) too. The PID output positive feedback (or negative feedback) signal will make the diffraction efficiency of AOM 1increases (or decreases), which means the power of the first-order diffraction light goes up (or down), and of zero-order diffraction light goes down (or up). Finally, we can achieve the purpose of Appl.suppressing Sci. 2020, 10the, 659 fluctuation of laser intensity. 9 of 11

5.2. The Suppression Results of Laser Intensity Fluctuation 5.2. The Suppression Results of Laser Intensity Fluctuation Figures 8 and 9 show the response of the feedback loop. The total power of the 1064-nm laser is 1.6 WFigures and the8 and sampling9 show power the response is 4.1 mW. of the The feedback light intensity loop. The fluctuation total power in the of thetime 1064-nm domain laser for the is 1.6free W-running and the case sampling and power feedback is- 4.1on mW. case The is light±3.360% intensity and fluctuation±0.064%, respectively. in the time domain The feedback for the free-running case and feedback-on case is 3.360% and 0.064%, respectively. The feedback bandwidth bandwidth in the frequency domain is 33± kHz, which ±covers the axial trap frequency and its double frequencyin the frequency of optical domain tweezer is 33, and kHz, is whichmuch coversbroader the than axial th trapat in frequencyour previous and works its double [13,17] frequency. There isof a optical strongtweezer, fluctuation and peak is much on 19.1 broader kHz, thandue to that the in fluctuation our previous from works the external [13,17]. environment. There is a strong The otherfluctuation four fluctuation peak on 19.1 peaks kHz, on due 5.9 to kHz the and fluctuation its double from frequency the external (11.8 environment. kHz), triple efficiency The other (17.7 four kHz)fluctuation and quadru peaksple on frequency 5.9 kHz and (23.6 its kHz) double are frequencycaused by (11.8YDFA’s kHz), cooling triple system. efficiency (17.7 kHz) and quadruple frequency (23.6 kHz) are caused by YDFA’s cooling system.

1.20 1.087 feedback off 1.18 (a) feedback on (b) Laser power 1.65 W@1064 nm, 1.086 Laser power 1.60 W@1064 nm, 1.16 sampling power 4.1 mW， sampling power 4.1 mW， intensity fluctuation ±3.360%. fluctuation ±0.064%. 1.14 1.085

1.12 1.084

1.10

1.083 1.08

Output voltage of sampling detector (V) detector sampling of voltage Output Laser power 1.60 W@1064 nm, sampling power 4.1 mW， feedback on

fluctuation ±0.064%. (V) detector sampling of voltage Output 1.06 1.082 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (min) Time (min) Figure 8. Intensity ﬂuctuation of laser in the time domain in the free-running case and the feedback-on Figure 8. Intensity fluctuation of laser in the time domain in the free-running case and the feedback- case. The light intensity is suppressed from 3.360% to 0.064%: 1.6 W for a total power of the 1064-nm on case. The light intensity is suppressed from± ±3.360%± to ±0.064%: 1.6 W for a total power of the 1064- Appl. laser,Sci. 2020 and, 10 the, x FOR sampling PEER REVIEW power is 4.1 mW (b), zooming of the feedback-on case in (a). 10 of 12 nm laser, and the sampling power is 4.1 mW (b), zooming of the feedback-on case in (a). 1E-4 FFT Spectrum Analyzer Bandwidth: 117 kHz feedback off Average: 16 times

1E-5 33 kHz

1E-6

Spectral density (V/√Hz) density Spectral Sampling power: 4.1 mW feedback on Detector: New Focus Model 2051 1E-7 Bandwidth: 1 kHz ~ 100 kHz Gain factor: 3 x

1 5 10 15 20 25 30 35 Analysis Frequency (kHz) FigureFigure 9.9. ComparisonComparison of of the the intensity intensity fluctuation fluctuation of laserof laser in thein the frequency frequenc domainy domain when when feedback feedback loop isloop on andis on o andff. The off. feedback The feedback bandwidth bandwidth in the in frequency the frequency domain domain is 33 is kHz. 33 kHz Several. Several noise noise peaks peaks are occurringare occurring from from the externalthe external environment environment or the or YDFA’sthe YDFA’s cooling cooling system. system. 6. Improvement of Atom Trapping Lifetime in Optical Tweezers 6. Improvement of Atom Trapping Lifetime in Optical Tweezers In the experiment, the power of the 852-nm cooling laser is 105 µw, the power of the 894-nm In the experiment, the power of the 852-nm cooling laser is 105 μw, the power of the 894-nm repumping laser is 50 µW, the quadrupole magnetic field intensity is 254 Gauss/cm, and the power of repumping laser is 50 μW, the quadrupole magnetic field intensity is 254 Gauss/cm, and the power the 1064-nm optical tweezers is 50 mW. Firstly, we capture a single-atom in the MOT and adjust the of the 1064-nm optical tweezers is 50 mW. Firstly, we capture a single-atom in the MOT and adjust spatial overlap of the MOT and the optical tweezer. We change the experimental sequence to control the spatial overlap of the MOT and the optical tweezer. We change the experimental sequence to the time overlap of the optical tweezer and the MOT for 25 ms, which maximizes the atomic transfer control the time overlap of the optical tweezer and the MOT for 25 ms, which maximizes the atomic efficiency between the MOT and the optical tweezer. Next, we measure the single-atom transfer transfer efficiency between the MOT and the optical tweezer. Next, we measure the single-atom efficiency under different time duration of the optical tweezer. As the duration of optical tweezer transfer efficiency under different time duration of the optical tweezer. As the duration of optical tweezer increases, atom transfer efficiency goes down exponentially. Finally, the single-atom trapping lifetime in the 1064-nm optical tweezer can be obtained by fitting measured data. As shown in Figure 10, the trapping lifetime of single-atom in the 1064-nm optical tweezer without the feedback loop on is only about 4.04 ± 0.92 s, while the trapping lifetime is 6.34 ± 0.41 s after the feedback loop is on. We can see that the trapping lifetime of single-atom in the optical tweezers is extended after the suppression of the intensity fluctuation of the optical tweezer.

90 100 -7 Pressure:~ 6×10 Pa Pressure:~ 6×10-7 Pa MOT: 80 (a) 90 MOT: Cooling beams：100 W (b) Cooling beams：100 W Repump beams：50 W ： 70 80 Repump beams 50 W Magnetic gradient：254.31 Gauss/cm Magnetic gradient：254.31 Gauss/cm Tweezer: Tweezer: 70 60 1064 nm power：50 mW 1064 nm power：50 mW 1/e Gaussian waist：2.2 m 1/e Gaussian waist：2.2 m 60 trap depth:：1.3 mK trap depth：1.3 mK 50 1/e trapping lifetime: 50 1/e trapping lifetime: 40 t ~ 4.04±0.92 s 40 t ~ 6.34±0.41 s

Figure 10. Trapping lifetime of atom in 1064-nm optical tweezer when the feedback loop is turned off (a) and on (b). The trapping lifetime of single-atom is extended from 4.04 s to 6.34 s.

The typical trapping lifetime here we achieved seems shorter than that of our previous work [19] because the background Cs density in the ultra-high vacuum (UHV) glass cell has increased a lot in this experiment. Now the trapping lifetime of single-Cs atom in the optical tweezer is mainly limited by the atomic collisions under the typical pressure of approximately 6 × 10−7 Pa. Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 12

1E-4 FFT Spectrum Analyzer Bandwidth: 117 kHz feedback off Average: 16 times

1E-5 33 kHz

1E-6

Spectral density (V/√Hz) density Spectral Sampling power: 4.1 mW feedback on Detector: New Focus Model 2051 1E-7 Bandwidth: 1 kHz ~ 100 kHz Gain factor: 3 x

1 5 10 15 20 25 30 35 Analysis Frequency (kHz) Figure 9. Comparison of the intensity fluctuation of laser in the frequency domain when feedback loop is on and off. The feedback bandwidth in the frequency domain is 33 kHz. Several noise peaks are occurring from the external environment or the YDFA’s cooling system.

6. Improvement of Atom Trapping Lifetime in Optical Tweezers In the experiment, the power of the 852-nm cooling laser is 105 μw, the power of the 894-nm repumping laser is 50 μW, the quadrupole magnetic field intensity is 254 Gauss/cm, and the power of the 1064-nm optical tweezers is 50 mW. Firstly, we capture a single-atom in the MOT and adjust the spatial overlap of the MOT and the optical tweezer. We change the experimental sequence to control the time overlap of the optical tweezer and the MOT for 25 ms, which maximizes the atomic Appl.transfer Sci. 2020 efficiency, 10, 659 between the MOT and the optical tweezer. Next, we measure the single10-atom of 11 transfer efficiency under different time duration of the optical tweezer. As the duration of optical tweezer increases, atom transfer efficiency goes down exponentially. Finally, the single-atom increases,trapping lifetime atom transfer in the e1064fficiency-nm optical goes down tweezer exponentially. can be obtained Finally, by the fitting single-atom measured trapping data. lifetime in theAs 1064-nm shown optical in Figure tweezer 10, the can trapping be obtained lifetime by fitting of single measured-atom data. in the 1064-nm optical tweezer withoutAs shown the feedback in Figure loop 10, theon is trapping only about lifetime 4.04 of ± single-atom0.92 s, while in the the trapp 1064-nming opticallifetime tweezer is 6.34 without± 0.41 s the feedback loop on is only about 4.04 0.92 s, while the trapping lifetime is 6.34 0.41 s after the after the feedback loop is on. We can ± see that the trapping lifetime of single-atom± in the optical feedbacktweezers is loop extended is on. Weafter can the see suppression that the trapping of the intensity lifetime fluctuation of single-atom of the in optical the optical tweezer. tweezers is extended after the suppression of the intensity fluctuation of the optical tweezer.

30 Free running (feedback control OFF) 30 Feedback control ON Sindle-photon transferring efficiency (%) efficiency transferring Sindle-photon Sindle-photon transferring efficiency (%) efficiency transferring Sindle-photon 1064 nm MOPA(DBR+YDFA)laser system 1064 nm MOPA(DBR+YDFA) laser system 20 20 0 5 10 15 20 0 2 4 6 8 10 12 14 1064 nm optical tweezer laser on time(s) 1064 nm optical tweezer laser on time(s) Figure 10. Trapping lifetime of atom in 1064-nm optical tweezer when the feedback loop is turned off Figure 10. Trapping lifetime of atom in 1064-nm optical tweezer when the feedback loop is turned off (a) and on (b). The trapping lifetime of single-atom is extended from 4.04 s to 6.34 s. (a) and on (b). The trapping lifetime of single-atom is extended from 4.04 s to 6.34 s. The typical trapping lifetime here we achieved seems shorter than that of our previous work [19] becauseThe the typical background trapping Cs lifetime density here in the we ultra-high achieved vacuumseems shorter (UHV) than glass that cell of has our increased previous a work lot in this[19] experiment.because the Nowbackground the trapping Cs density lifetime in of the single-Cs ultra-high atom vacuum in the optical (UHV) tweezer glass cell is mainlyhas increased limited a lot in this experiment. Now the trapping lifetime of single-Cs atom in7 the optical tweezer is by the atomic collisions under the typical pressure of approximately 6 10− Pa. mainly limited by the atomic collisions under the typical pressure of× approximately 6 × 10−7 Pa. 7. Conclusions In this paper, we analyzed how the background pressure in the atomic vapor cell and the intensity fluctuation of optical tweezers act on the atomic trapping lifetime and suppressed the intensity fluctuation of the 1064-nm optical tweezer to extend the trapping lifetime of single-atom. The suppression bandwidth will be extended to cover the trap frequency and its double frequency on the both axial and radial direction. In addition, the suppression effect of laser intensity fluctuation in the time domain and the feedback bandwidth in the frequency domain can be adjusted to meet different experimental requirements, which would provide valuable insights for subsequent experiments of single-atom manipulation and quantum simulation.

Author Contributions: The experiment and data were completed by R.S., X.W. and K.Z.; J.H. undertook partial guidance during the experiment. And J.W.’s contributions included coordination, guidance and data analysis in the experiment; R.S. and J.W. wrote and revised the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by [The National Key R & D Program of China] grant number [2017YFA0304502], [the National Natural Science Foundation of China] grant number [11774210, 6187511, 11974226 and 61905133], and [Outstanding Graduate Innovation Program of Shanxi Province] grant number [2019BY2016]. Conﬂicts of Interest: There is no conﬂict of interest in this article.

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