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arXiv:1804.07044v1 [quant-ph] 19 Apr 2018 vrawd rqec ag rm10Mz[]t over to [6] fields MHz 100 electric from of range properties wide been the a has over measure cell vapor induced to in electromagnetically employed [5] Rydberg (Rydberg-EIT) calibration-free transparency potentially 4]. and [3, be- traceability operation electrometry, SI traditional of over cause advantages metrology clear field has Rydberg-atom-based properties, atomic et ( ments iieeeti edsnos u oterlrepolariz- large their to due ( sensors, abilities field electric sitive numbers quantum [1]. communication been classical already for have quan- explored fields electro-magnetic atom-based for Recently, sensors tum tasks. specialized communications are atom-based for that in novel components into receiver surge and lead recent naturally A will detection atom-based for field technologies circuit. quantum of an- development an the MHz. a includes hundred and typically several frequency unit tenna to receiving carrier kHz - the of The in hundreds instance, from radio For ranges FM (FM). and via AM frequency wave or carrier electromagnetic (AM) an sig- onto continu- a nal are of modulation/demondulation and on based communication defense, Typically, is and further. developed science being life, ously social in role ∗ orsodn uhr [email protected] author: Corresponding ybr tm,hgl xie tm ihprincipal with atoms excited highly atoms, Rydberg increasing ever an play technologies Communication tmbsdqatmrcie o mltd-adfrequency- and amplitude- for receiver quantum Atom-based ucu Jiao Yuechun ∝ ∝ n ewrs ybr I,A pitn,ao-ae unu se quantum atom-based splitting, AT EIT, Rydberg 84.40.-x, Keywords: 42.50.Gy, 32.80.Ee, numbers: sa PACS spectroscopic faster by increased be can demonstration, aeadsga ouae noa1.8Gzcrirwv in wave communicati carrier microwave for 16.98-GHz suitable a receiver onto quantum based modulated baseband a ftecrirwv eut nacrepnigmdlto in t modulation of height corresponding relative a in change in a causes results modulation o wave Frequency splitting carrier (AT) the Autler-Townes of an in resulting transition, osntrqieeetoi eouain h ehdi sui is method The demodulation. from electronic range T require signal. not modulation the does retrieve to processed and detected ae-pcrsoi ehd h irwv are sreso is carrier microwave The method. laser-spectroscopic tm ntecl stakdvaeetoantclyinduce electromagnetically via tracked is cell the in atoms 2 3 n 2 olbrtv noainCne fEteeOtc,Shanxi Optics, Extreme of Center Innovation Collaborative 2.Det h nain aueof nature invariant the to Due [2]. ) notclpoeo eimRdegaosgnrtdi therm a in generated atoms Rydberg cesium of probe optical An 7 eateto hsc,Uiest fMcia,AnAbr M Arbor, Ann Michigan, of University Physics, of Department n irwv-rniindpl mo- dipole microwave-transition and ) .INTRODUCTION I. 1 , n 3 iounHan Xiaoxuan , ≫ nttt fLsrSetocp,Sax nvriy Taiyu University, Shanxi Spectroscopy, Laser of Institute ∼ 1 tt e aoaoyo unu pisadQatmOtc De Optics Quantum and Optics Quantum of Laboratory Key State H ohnrd fGz h aeadbnwdh hc is which , baseband The GHz. of hundreds to GHz 1 ,cnb sdt raesen- create to used be can 1, inl nhg-rqec ai communication radio high-frequency in 1 , 3 ibiFan Jiabei , 1 , 3 er Raithel Georg , are i mltd rfeunymdlto.The ce- the microwave modulation. with 60 GHz interacts sium frequency 16.98 resonantly or a carrier on amplitude high-frequency demonstra- range) via 10-Hz experimental (band- carrier signal the our baseband in low-frequency width In a high- encode a we real-time onto tion, enable encoded carrier. in can of frequency which atoms readout direct Rydberg cell, and on room-temperature based a communication crowave 15]. imaging [14, subwavelength distributions for electric-field Rydberg microwave used of addition, be In can receivers operation. atomic parallel potential high-speed them with for making communication long-distance [13], detec- antennas for than suitable dipole sensitivity traditional higher with frequen- a have tors of can set Rydberg-atom-based detectors dense field a THz-range. to at MHz- the atoms within electromag- these cies strong of a response to tran- leading netic electric-dipole elec- [2], of many them number between have large sitions a atoms with states Rydberg tronic digital [12]. for receivers communication high communications sensitive, as atomic explored bandwidth, been Recently, also have miniaturization. atoms millimeter for Rydberg em- potential and that significant offer sensors [9], field polarizations Rydberg-atom ploy Small their [10]. (MW) and microwave of [8] measurements fields including [7], THz 1 eso H ag.Etnint are rqece in carrier to mi- Extension the for range. in element GHz frequency receiver of carrier tens a and with sensor communication consti- crowave quantum a This tutes (Rydberg-EIT-AT). Ryd- effect the the Autler-Townes and employing by electromagnetically-induced-transparency recovered berg is information coded nti ok epooeaqatmsno o mi- for sensor quantum a propose we work, this In µ atwt h 60 the with nant h I inl mltd modulation Amplitude signal. EIT the f eotclrtivlo h aeadsignal baseband the of retrieval optical he sro eevr irwv communication microwave receiver, or nsor mpling. -eghvprclsadhlo-oefies[11] fibers hollow-core and cells vapor m-length etoA ek,wihcnb optically be can which peaks, AT two he n h 60 The on. S rnprny(I) nestablished an (EIT), transparency d 1 1 al o are rqece ihna within frequencies carrier for table , h pial eree Tsplitting. AT retrieved optically the nvriy aya 306 China 030006, Taiyuan University, 2 / inigZhao Jianming , 2 eltm,dmntaiga atom- an demonstrating real-time, → cia 80-10 S and USA 48109-1120, ichigan lvprcl sue oretrieve to used is cell vapor al 60 n000,China 030006, an S P 1 / 1 2 / S 2 ybr ee fcesium of level Rydberg 1 ∼ / ybr rniin n h en- the and transition, Rydberg 2 ouae baseband modulated 0H ntepresent the in Hz 20 → 1 vices, , 60 3 , ∗ P 1 n utn Jia Suotang and / 2 Rydberg 1 , 3 2

is applied transversely to the laser beams propagating through the vapor cell, where it interacts with cesium receiver Rydberg atoms. A baseband signal function is amplitude- or frequency-modulated onto the carrier mi- crowave. The MW carrier has a frequency of 16.98 GHz, which drives the 60S1/2-60P1/2 Rydberg transition with an on-resonance Rabi frequency Ω. The resultant EIT- AT splitting spectra, a sample of which is shown in Fig. 1(c), are used as a real-time optical readout of the modulation signal that is encoded in the MW.

FIG. 1. (a) Schematic of the experimental setup. The cou- 60

(a) pling and probe beams, with respective wavelengths λc and 50 λp, counter-propagate through and overlap within a cesium

vapor cell. The probe beam is passed through the cell and 40 a dichroic mirror (DM), and is detected with a photodiode

(PD), yielding the probe transmission. The microwave field 30

(MW) has a carrier frequency of 16.98 GHz and is amplitude- (MHz)AT Splitting or frequency-modulated with a low-frequency baseband sig- 20

nal; the modulation contains the transmitted information. Transmitted AM signal, m

(b) AM

The modulated MW signal is fed into a horn and Received AM signal, m

Rec radiated into the atomic cell, which receives the signal. The 1.5 laser and microwave electric fields have the same polariza-

tion, transverse to the drawing plane. (b) Four-level Rydberg- 1.0 EIT scheme. The microwave field is (near-)resonant with the 60S1/2 → 60P1/2 Rydberg transition. The resultant AT split- ting is measured and used as a real-time, optical readout for 0.5 the modulation signal. (c) Samples of measured EIT spec- 0 1 2 3 4 5 tra with MW off (black solid line) and on (red dashed line) Transmitted and Received Signals Time (s) vs coupler-laser detuning, ∆c. In the displayed on-resonant case, the AT splitting observed with the MW on, fAT , ap- FIG. 2. results for sinusoidal mod- proximately equals the Rabi frequency of the MW transition, ulation. (a) Measurement of the AT splitting, fAT (t). (b) Ω. Comparison between the amplitude modulation function ap- plied to the microwave generator, mAM (t) (transmitted base- band signal; black line), and the corresponding received sig- the hundreds of MHz to 1 THz range is straightforward. nal, mRec = Ecm(t)/Ec (stars), which is derived from the spectroscopically acquired AT splitting shown in (a). For the case shown, ωs = 2π × 1 Hz, Ec = 2.25 V/m and − II. EXPERIMENTAL SETUP mAM (t) = 1 0.50 cos(ωst).

A schematic of the experimental setup and the rele- vant four-level system are shown in Figs. 1 (a) and (b). The experiments are performed in a room-temperature III. AMPLITUDE MODULATION cesium vapor cell. The coupling and probe beams are overlapped and counter-propagated along the centerline In our initial demonstration, the signal to be transmit- of the cell. A 852-nm (λp) probe laser, resonantly in- ted is an amplitude-modulated signal function mAM (t)= teracting with the lower transition, |6S1/2, F = 4i → 1−k cos(ω t) with a signal frequency ω and modula- ′ AM s s |6P3/2, F =5i with Rabi frequency Ωp =2π×12.3 MHz, tion index kAM . Denoting the carrier frequency ωc and and beam waist w0 = 105 µm, and a 510-nm (λc) cou- the fixed (unmodulated) field amplitude Ec, the modu- pling beam, scanning through the Rydberg transition lated MW field impinging onto the atoms in the vapor ′ |6P3/2, F = 5i → |60S1/2i with Ωc = 2π×2.45 MHz cell is and w0 = 150 µm, form the Rydberg-EIT system that is employed to measure the modulated microwave field. EAM (t)= EcmAM (t) cos(ωct). (1) The power of the probe beam passing through the cell is detected with a photodiode and recorded with an oscil- The modulated field amplitude, Ecm(t) = EcmAM (t) loscope. This yields an all-optical readout for the field = Ec(1 − kAM cos(ωst)), is proportional to the signal strength and the frequency of the microwave field as a function mAM (t) to be transmitted. On the receiver end, function of time. the objective therefore is to measure Ecm(t) by rapid The MW field, generated with a acquisition and analysis of Rydberg-EIT-AT spectra. A (Keysight N5183) and emitted from a horn antenna, sample of such a is shown in Fig. 1(c). Denoting 3

Transmitted AM signal, m

AM the measured slowly-varying AT splitting frequency by (a)

Received AM Signal, m fAT , we retrieve Ecm(t) using the relation Rec

1.5 ~ Ecm(t)=2π fAT (t) (2) ℘ 1.0 ~ where is Planck’s constant and ℘ is the atomic dipole 0.5 moment of the MW transition (here, ℘ = 1.046 ×

−26 (b) 10 Cm). For Eq. 2 to approximately hold, the car- 1.5 rier frequency must be resonant with the desired Rydberg transition (here 60S1/2-60P1/2), and other conditions ap-

1.0 ply [4]. Also, to recover the signal function mAM (t) in Transmitted and Received Signals real time, the spectrum acquisition time must be much

shorter than 2π/ωs. 0.5 In Fig. 2(a) we show the measured AT splitting,

0 1 2 3 4 5 fAT (t), which yields the MW field amplitude Ecm(t) Time (s) according to Eq. 2. For the case in Fig. 2(a), the modulation-free electric field of the carrier is determined FIG. 3. Amplitude modulation results for square (a) and to be 2.25 V/m. When the modulation is applied, the complex (b) baseband modulation functions. Black solid sinusoidal oscillation of the detected MW field normal- lines show the transmitted functions, mAM (t), and stars with vertical drop lines show the received signals, m (t)= ized by the carrier field, mRec(t) = Ecm(t)/Ec, directly Rec Ecm(t)/Ec, derived from spectroscopically acquired AT split- reproduces the applied modulation function mAM (t). To tings. show that the retrieved signal mRec(t) equals the applied modulation signal mAM (t), in Fig. 2(b) we compare both functions. Overall we observe good agreement, as ex- pected. We determine the deviation between the trans- berg EIT-AT spectroscopy also can be used as a quantum receiver to retrieve information in FM-modulated signals. mitted and received signals, |mAM (t) − mRec(t)|, to be . 5% of the average transmitted signal and a fidelity of In FM-mode, the microwave field has a fixed amplitude the recovered signal of & 95%. Ec and a time-dependent phase Φ that carries the signal, For the case of sinusoidal , data as shown in Fig. 2 also allow rapid retrieval of the modulation fre- EF M (t)= Ec cos(ωct + Φ(t)) (4) quency, ωs, and the modulation index. For instance, in with the signal Φ(t). The transmitted Fig. 2 the minima and maxima of the retrieved Ecm(t) FM signal is the time derivative of the phase, δωF M (t)= are Ecm,min =1.13 V/m and Ecm,max = 3.38 V/m, yield- ′ ing a reading for the modulation index of the transmitted Φ (t). Typically the baseband signal to be sent is pro- portional to δω (t). For instance, for a pure acoustic and received signals, mAM (t) and mRec(t), of F M tone in the baseband, the function δωF M (t) varies sinu- Ecm,max − Ecm,min soidally at the frequency of the tone, and the amplitude kAM ≈ , (3) Ecm,max + Ecm,min of the function δωF M (t) is proportional to the square root of the sound intensity. For the present discussion, which is kAM =0.50 in Fig. 2. the FM-signal retrieval task amounts to extracting the To test the time resolution and the transmission transmitted function δωF M (t) from experimentally ac- bandwidth of the method, we have also investigated quired Rydberg-EIT-AT spectra. square and structure-rich amplitude modulation func- Our method relies on the fact that the shape of the tions mAM (t). These have a repetition frequency of Rydberg-EIT-AT spectra changes as a function of the 1 Hz, with a much higher signal bandwidth (because of FM baseband signal function δωF M . In Fig. 4, we present the sharp features in the functions). Fig. 3 shows that calculated spectra for several fixed values of the detuning the transmitted and received modulation functions agree δωF M = 2π× 0 MHz and ± 40 MHz, respectively. The very well in both cases. From the lag and the deviations carrier frequency ωc is chosen such that for δωF M = 0 seen at the steps, we estimate a transmission bandwidth the microwave field is resonant with the Rydberg transi- in the baseband of ∼ 20 Hz, for the cases shown. tion used for the detection. In the present demonstration we use a carrier frequency ωc = 16.98 GHz, which is res- onant with the 60S1/2-60P1/2 transition. For δωF M = 0, IV. the EIT-AT spectrum exhibits two symmetric lines. As the detuning δωF M is tuned away from resonance, the In , FM modulation is often prefer- line separation increases and the line heights become able to AM modulation because FM offers a higher band- asymmetric. It is found, in particular, that the detuning width and is more resilient to interference and carrier- δωF M (t) is a single-valued function of the relative line- strength fluctuations. In this section we show that Ryd- height difference, F = (H+ − H−)/(H+ + H−), where 4

= 0 MHz of the atoms to the microwave. In the retrieval process,

MW 0.06

= -40 MHz MW Rydberg-EIT-AT spectra are acquired and analyzed at

0.05 = 40 MHz MW a rate higher than 1/ωs. In Fig. 5(a) we compare the

0.04 transmitted FM signal δωF M (t) and the received signal δωRec(t) obtained from Eq. 5. The figure shows that

0.03 δωRec(t) ≈ δωF M (t), demonstrating successful atom-

0.02

EIT signal (arb.units) signal EIT based FM reception of a 1-Hz sinusoid. In Fig. 5(b) we re-

0.01 peat the procedure for an arbitrary modulation function that has a higher signal bandwidth in the baseband. We

0.00

-100 -80 -60 -40 -20 0 20 40 60 80 100 again see good agreement between δωF M (t) and δωRec(t),

/2

c demonstrating the viability of atom-based FM reception for higher baseband bandwidths (here, ∼ 20 Hz).

FIG. 4. Calculated Rydberg-EIT-AT spectra for MW fields 1 2 → 1 2 interacting with the 60S 60P Rydberg transition. 60 / / Transmitted modulation signal × (a) The Rabi frequency of the MW transition is Ω = 2π 40 MHz, Received Signal and the frequency detunings are δωFM = 0 (black solid line), 40 +40 MHz (blue dashed line) and -40 MHz (red dot-dashed

20 line), respectively. For δωFM = 0 the EIT-AT spectra exhibit

two symmetric AT lines, while for non-zero detuning the AT 0 lines become asymmetric in height. The (signed) difference

-20 in height yields an unambiguous reading for δωFM .

-40 (MHz)

40 + − Transmitted modulation signal H and H are the heights of the higher- and lower- (b) frequency Rydberg-EIT-AT peaks relative to the read- Received Signal ing away from the AT peaks. Assuming that the AT- 20

peak line strengths are proportional to the squares of the 0 60S1/2-components in the corresponding AT eigenstates, we find by a straightforward analysis that the transmit- -20 ted baseband signal δωF M (t) can be retrieved from the function F via the relation -40

−F (t)Ω 0 1 2 3 4 5 δωRec(t)= , (5) p1 − F (t)2 Time (s) where Ω is the Rabi frequency of the microwave tran- FIG. 5. Comparisons of transmitted and received FM sig- sition between the Rydberg levels. Ideally, δωRec(t) = nals, δωFM (t) (black lines) and δωRec(t) (symbols with verti- δωF M (t). Equation 5 is applicable if the transmitted FM cal drop lines) for (a) sinusoidal and (b) arbitrary FM modu- lation. The modulation frequency is 2π×1 Hz, the MW Rabi modulation signal δωF M (t) varies slowly enough to allow frequency used in Eq. 5 is Ω = 2π × 60 MHz, and the maxi- for real-time acquisition of the Rydberg-EIT-AT spec- ≈ × trum and extraction of the quantity F (t). The Rydberg- mum absolute values of δω are 2π 40 MHz. EIT-AT spectra are acquired in rapid succession, and the line heights H+(t) and H−(t) are extracted in real-time. The function F = (H+ − H−)/(H+ + H−) and Eq. 5 are V. DISCUSSION AND CONCLUSION then used to calculate the received detuning δωRec(t). This completes the FM signal retrieval task. It is noted that the only requirement for the spectroscopic readings Figures 2, 3 and 5 demonstrate that Rydberg EIT-AT H+ and H− is that they must be proportional to the EIT- in an atomic vapor can be employed as a quantum sensor induced change of the transmission of the atomic vapor that enables real-time and direct readout of AM and FM for the probe light. Also, the Rabi frequency Ω in Eq. 5 baseband signals modulated onto electromagnetic carrier is given by the modulation-free splitting between the AT waves in the GHz range. For detecting AM-modulated peaks (i.e. the splitting seen at δωF M = 0). baseband signals, we employ the fact that on-resonant To demonstrate retrieval of an FM signal, in Fig. 5(a) AT splittings depend linearly on the MW amplitude, we apply a sinusoidal FM modulation (transmitted FM as seen in Eq. 2. For the AM test signals we use in signal) to the microwave interacting with the atoms, Figs. 2(b), 3(a) and 3(b), whose complexity is increas- δωF M (t) = −A cos(ωst) with an FM modulation fre- ing in that order, we find average deviations between the quency ωs = 2π × 1 Hz and modulation amplitude transmitted and retrieved AM signal functions of 5.0%, A = 2π× 40 MHz. The objective of the FM signal re- 1.6% and 5.7%, corresponding to fidelities of 95% and trieval then is to recover the function δωF M (t), and its 98.4% and 94.3%. parameters ωs and A, from the spectroscopic response In FM modulation the Rydberg EIT-AT spectra are 5 asymmetric, with the height difference between the two an electronic demodulation process. The range of carrier AT peaks providing a direct readout for the FM base- frequencies that can, in principle, be employed is quite band signal. In our demonstration for a sinusoidal and vast. This is because strong electric-dipole transitions an arbitrary baseband signal, the respective deviations between conveniently accessible Rydberg levels span a of the readout from the baseband signal are about 3.0% frequency range from . 1 GHz up to ∼ 1 THz. The and 6.3%, corresponding to fidelities of about 97% and signal bandwidth in the baseband used in this work is 93.7%. ∼ 10 Hz. It is expected that this can be increased to sev- eral kHz using a faster data acquisition method for the In both the AM and FM case, the deviations are mostly spectroscopic data. attributed to the limited sampling rate of data-taking The work was supported by the National Key R&D system, the laser frequency jitter, and the intrinsic EIT Program of China (Grant No. 2017YFA0304203), the linewidth. The nonlinear dependence of the AT splitting National Natural Science Foundation of China (Grant on the microwave Rabi frequency [4] may also affect the Nos. 61475090, 61675123, 61775124), the Changjiang fidelity. Scholars and Innovative Research Team in University of Our work paves the way towards the employment of Ministry of Education of China (Grant No. IRT13076), atom-based quantum sensors and receivers in the Key Program of the National Natural Science Foun- atom-based microwave communications. The method dation of China (Grant No. 11434007) and Shanxi 1331 could outperform traditional communications techniques Project Key Subjects Construction. GR acknowledges that involve large receiver antennas. The signal recovery support by the NSF (PHY-1506093) and BAIREN plan from the atom-based spectroscopic data does not require of Shanxi province.

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