Coupling Rydberg to microwave fields in a superconducting coplanar waveguide resonator

A. A. Morgan and S. D. Hogan Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom (Dated: September 21, 2020) Rydberg helium atoms traveling in pulsed supersonic beams have been coupled to microwave fields in a superconducting coplanar waveguide (CPW) resonator. The atoms were initially prepared in 3 3 the 1s55s S1 Rydberg level by two-color two- laser excitation from the metastable 1s2s S1 3 3 level. Two-photon microwave transitions between the 1s55s S1 and 1s56s S1 levels were then driven by the 19.556 GHz third-harmonic microwave field in a quarter-wave CPW resonator. This superconducting microwave resonator was fabricated from niobium nitride on a silicon substrate and operated at temperatures between 3.65 and 4.30 K. The populations of the Rydberg levels in the experiments were determined by state-selective pulsed electric field ionization. The coherence of the -resonator coupling was studied by time-domain measurements of Rabi oscillations.

Hybrid quantum systems, composed of individual com- ronments. These studies were performed using helium ponents with complementary characteristics, e.g., coher- (He) atoms to minimize adsorption, and associated time- ence times, state manipulation rates, available transition dependent changes in stray electric fields emanating from frequencies, or scalability, are of interest in a range of ar- the surfaces [12]. Subsequently, proposals were put for- eas, from quantum computation and communication to ward to implement quantum gates [13, 14], quantum- quantum sensing (see, e.g., Refs. [1–3]). Initial proposals state transfer [15, 16], and microwave-to-optical photon to use gas-phase atoms or molecules as quantum memo- conversion [17, 18], and to access new regimes of light- ries and optical interfaces for solid-state quantum proces- matter interactions [19] in hybrid systems composed of sors [4] were conceived to combine (1) the long-coherence Rydberg atoms and superconducting circuits. Transi- times of transitions between rotational states in polar tions between Rydberg states have have been driven by molecules with electric dipole moments of ∼ 1 e a0 (e and microwave fields propagating in superconducting copla- a0 are the charge and Bohr radius, respectively), nar waveguides [20, 21], and ground-state rubidium and (2) the scalability and fast quantum-state manipula- atoms have been coupled to microwave fields in super- tion achievable in solid-state superconducting circuits [5]. conducting CPW resonators [22]. However, up to now Coupling between these systems was envisaged using coupling between Rydberg atoms and microwave fields chip-based superconducting coplanar waveguide (CPW) in CPW resonators has not been reported. microwave resonators [5, 6]. Atoms in Rydberg states Here we present the results of experiments in which with high , n, are also well Rydberg atoms, in particular He atoms initially prepared 3 suited to this approach to hybrid microwave cavity quan- in the 1s55s S1 (|55si) level, have been coupled to mi- tum electrodynamics (QED), and have played a central crowave fields in a chip-based superconducting CPW res- role in many seminal cavity QED experiments with three- onator, with a mode volume ∼ 10−6 times smaller than dimensional microwave cavities (see, e.g., Ref. [7], and that of any resonator used previously in microwave cavity references therein). In the hybrid cavity QED setting, the QED experiments with atoms in Rydberg states [23, 24]. large electric dipole moments associated with microwave These fields, at frequencies close to 19.556 GHz, were res- transitions between Rydberg states (typically > 1000 e a0 onant with the 1s55s 3S →1s56s 3S (|55si → |56si) two- > 1 1 for n ∼ 30 [8]) offer higher single-particle atom-resonator photon transition. These |nsi Rydberg states are appro- arXiv:1911.05513v2 [quant-ph] 18 Sep 2020 coupling strengths than ground-state molecules. These priate for directly interfacing microwave in the can be achieved while maintaining a wide range of avail- superconducting circuit with optical photons for long- able transition frequencies for applications in optical-to- distance information transfer. The methods employed microwave photon conversion [9, 10], and – in the case of could be implemented with long-lived circular Rydberg circular Rydberg states – lifetimes > 10 ms for quantum states in He [25] for use as quantum memories. This memories. hybrid cavity QED system is of interest in accessing of The development of hybrid approaches to cavity QED new regimes of light-matter interactions [19], and for non- with Rydberg atoms and microwave circuits began with demolition detection [23, 24] of cold trapped Rydberg experiments in which |nsi → |npi transitions were driven molecules [26], and Rydberg positronium atoms [27]. by microwave fields in copper CPWs [11]. This high- A schematic diagram of the experimental apparatus lighted effects of stray electric fields emanating from the is displayed in Fig. 1(a). A pulsed supersonic beam of 3 surfaces of the microwave circuits that must be consid- He atoms (hvHei = 2000 m/s) in the metastable 1s2s S1 ered in these experiments performed in cryogenic envi- level was generated in an electric discharge at the exit of 2

(a) cal temperature Tc = 12.1 K) superconducting CPW 30 K heat shield 4 K heat shield microwave resonator [Fig. 1(b)]. This resonator was fabricated by photolithography of a 100-nm-thick NbN E3 E4 film on a 10 mm×10 mm silicon chip. The resonator was L-shaped with a length of 6.335 mm, and center- E2 conductor and insulating gap widths of w = 20 µm and E5 c wg = 10 µm, respectively [see inset in Fig. 1(b)]. At

vHe the open end, the resonator was capacitively coupled to a U-shaped superconducting CPW. The center conduc- Metastable tor and ground planes of this CPW were electrically con- He beam Chip holder nected to a larger copper CPW on a printed circuit board y E1 [Fig. 1(a)]. The resonator was operated at temperatures z UV and IR MCP detector laser beams close to TCPW = 3.65 K for which its third-harmonic fre- x quency was ν3 = 19.559 41 GHz, loaded quality factor (b) was Qloaded = 2280, and build-up/ring-down time was C τ = 18.4 ns. A λ/4 CPW resonator geometry, with one 120 μm 100 μm grounded end and one open end, was chosen to minimize

wc wg charge buildup on the center conductor. As the Rydberg atoms traveled along the 4.858-mm- 100 μm long section of the resonator aligned with the axis of v Resonator He propagation of the atomic beam [see Fig. 1(b)], the res-

10 mm C onant enhancement in the local microwave field was ex- x dimension ploited to drive two-photon |55si → |56si transitions at Waveguide ν55s,56s/2 = 19.556 499 GHz. 16 mm beyond the NbN chip the atoms were detected by state-selective pulsed electric field ionization by applying a slowly-rising pulsed ionization potential of −125 V to E4 while E5 was main- tained at 0 V. Ionized were accelerated through 10 mm z dimension a 5-mm-diameter aperture in E5 and out of the cryogenic region to a room-temperature microchannel plate (MCP) FIG. 1. (a) Schematic diagram of the experimental apparatus detector [Fig. 1(a)]. (not to scale). For clarity parts of the heat shields and elec- The triplet |55si (|56si) in He has a trode E3 have been omitted. (b) Diagram of the 10 × 10 mm of 0.296 669 3 (0.296 668 8) [30]. As NbN chip containing a U-shaped CPW and an L-shaped λ/4 seen in Fig. 2(a) this state exhibits a quadratic CPW resonator along which the atomic beam propagated. Stark shift in weak electric fields, with a static The inset in (b) represents an expanded view of the coupling 2 region, C, between the waveguide and resonator. electric dipole of 1.955 45 GHz/(V/cm) [2.202 11 GHz/(V/cm)2]. The small difference between the |55si and |56si means that the |55si → |56si transition has a low sensitivity to residual un- a pulsed valve (repetition rate 50 Hz) [28]. After pass- canceled stray electric fields, and electric field inhomo- ing through a 2-mm-diameter skimmer and a charged- geneities. This can be seen from the Stark shift of particle filter, the atoms entered through apertures of 4 ν55s,56s/2 in fields up to 120 mV/cm in Fig. 2(b). and 3 mm diameter in two heat shields, maintained at To couple Rydberg atoms to the microwave field in the 30 K and < 4 K, respectively, and into the cryogenic CPW resonator the apparatus in Fig. 1(a) was cooled to region. Between two electrically isolated parallel cop- cryogenic temperatures following a procedure similar to per blocks, E1 and E2 in Fig. 1(a), the atoms were ex- that in Ref. [31]. Throughout the cooling process the 3 3 cited to Rydberg states using the 1s2s S1 → 1s3p P2 → NbN chip was maintained at a higher temperature than 3 1s55s S1 two-color two-photon excitation scheme [29]. the other components to minimize adsorption. The res- This was driven with focused (∼ 100 µm FWHM beam onator was then stabilized to TCPW = 3.65 K so that waist) co-propagating continuous wave (CW) laser ra- ν3 = 19.559 41 GHz. When the Rydberg atoms passed diation at of 388.975 nm and 786.817 nm, over the first antinode of the microwave field, 13.25 µs respectively, in a pulsed electric field of 0.3 V/cm. This after photoexcitation, a 500-ns-long pulse of microwave field was switched on for 1.25 µs generating 2.5-mm-long radiation at the frequency ν55s,56s/2, and a CW output bunches of Rydberg atoms. power at the source of Psource = 2 mW (the attenuation After excitation the atoms traveled 25 mm to the between the source and the CPW on the NbN chip was grounded end of a λ/4 niobium nitride (NbN) (criti- ∼ −22.5 dB), was injected into the resonator to drive 3

(a) (a) -1.05 0.0 |56p〉 4.30 K -1.0 -1.06 4.10 K |56s〉 (dB) 3.65 K 2 3.90 K

/ -2.0 -1.07 Transmission

55s,56s 19 500 19 520 19 540 19 560 19 580

ν h (THz)

/ (b) -1.08 1.0 (i) TCPW = 3.65 K 2

/ n = 55 0.5 -1.09 55s,56s Energy

ν |55p〉 0.0 -1.10 |55s〉 1.0 (ii) TCPW = 3.90 K -1.11 0.5 01234 (V/cm) 0.0 (b) 0.0 1.0 (iii) TCPW = 4.10 K 2 h

/ 0.5 -0.5 55, 56

(MHz) 0.0 ∆ E - 19556.499 -1.0 1.0 T = 4.30 K 020406080 100 120 (iv) CPW Electric field (mV/cm) 0.5 Normalized |56s 〉 electron signal (arb. units) FIG. 2. (a) Stark map of the triplet Rydberg states in He with 0.0 m` = 0. The two-photon |55si → |56si transition is indicated -8 -6 -4 -2 0 +2 +4 +6 +8 by the vertical red arrows. (b) Electric-field dependence of the |55si → |56si two-photon transition frequency. Frequency - 19 556.350 MHz

FIG. 4. (a) Temperature dependence of resonator line shape recorded by monitoring the CPW transmission. (b-i)–(b-iv) Spectra of the |55si → |56si two-photon transition recorded for P = 2 mW and the values of T indicated. Ex- 1.0 source CPW perimentally recorded (calculated) data are indicated by the blue points (dashed red curves). 0.8

0.6 the |55si → |56si transition. To compensate stray elec- 0.4 tric fields above the NbN chip, the population transfer from the |55si to the |56si state, driven by this resonator field, was monitored while a pulsed potential, Vcomp, ap- signal (arb. units) 0.2 〉 plied to E3 was adjusted. The resulting data in Fig. 3

|56s indicate that maximal population transfer occurred for 0.0 Vcomp ' +1.45 V. With this potential applied to E3, the electric field at the position of the atoms was therefore -0.2 minimized. This compensation potential was applied for 0.0 0.5 1.0 1.5 2.0 Pulsed potential, V (V) all subsequent measurements. comp The coupling of the atoms to the microwave field in the resonator was confirmed by recording spectra for a FIG. 3. Dependence of the population transfer to the |56si range of detunings of ν3 from ν55s,56s/2. The value of state on the potential, Vcomp, applied to electrode E3 to com- pensate stray electric fields close to the NbN chip surface. In ν3 is strongly dependent on TCPW. This can be seen recording this data TCPW = 3.65 K, and the resonator was from the spectra of microwave transmission through the driven with a microwave field at the frequency ν55s,56s/2. U-shaped CPW on the NbN chip in Fig. 4(a). The mea- sured resonances exhibit asymmetric line shapes as a re- sult of interference between the transmitted microwave 4

TCPW (K) ν3 (GHz) Qint Qloaded 1.0 3.65 19.559 41 2900 ± 135 2280 ± 90 Experiment 3.90 19.551 11 2635 ± 130 2140 ± 90 Calculation 0.8 4.10 19.542 61 2650 ± 110 2200 ± 80 4.30 19.533 99 2720 ± 115 2390 ± 90 Δ = 0 MHz 0.6 TABLE I. Temperature dependence of ν3, and the internal, Qint, and loaded, Qloaded, quality factors of the CPW res- population onator determined from the spectral function representing the 〉 0.4 microwave transmission through the waveguide displayed in Fig. 4(a). |56s Δ = +2 MHz 0.2

field, and that scattered by the resonator. The val- 0.0 ues of ν3, and the internal, Qint, and loaded, Qloaded, 0 100 200 300 400 500 quality factors of the resonator, i.e., the quality fac- Microwave pulse duration (ns) tor of the isolated resonator, and the modified quality factor arising as a result of the coupling to the waveg- FIG. 5. Rabi oscillations in the population of the |56si state uide, determined from these spectra using the circle-fit recorded for Psource = 12.6 mW and the driving microwave method [32] are listed in Table I. For T = 3.65 K, field on resonance with, and detuned by +2 MHz from, CPW ν /2 as indicated. For both measurements, T = ν = 19.559 41 GHz and the resonator resonance had a 55s,56s CPW 3 3.65 K. FWHM spectral width of 8.5 MHz. A microwave spec- trum of the |55si → |56si transition recorded under these conditions, with 500-ns-long microwave pulses injected into the resonator and Psource = 2 mW, is displayed in Psource = 12.6 mW, and the |56si signal, normalized Fig. 4(b-i) (blue points). The centroid of the observed to the total Rydberg atom signal, was monitored while spectral line lies at 19.556 350 GHz, and its width is the duration of the microwave pulse injected into the ∆νFWHM ' 1.4 MHz. Comparing this measured transi- resonator was adjusted. For ∆ = 0 MHz (open cir- tion frequency with ν55s,56s/2, and the data in Fig. 2(b), cles in Fig. 5) up to 60% population transfer to the indicates that the average stray electric field at the posi- |56si state was observed, but the Rabi oscillation fre- tion of the atoms above the resonator was < 50 mV/cm. quency of ∼ 3 MHz permitted the observation of only When ν3 was detuned from ν55s,56s/2 the enhancement in one complete Rabi cycle within the coherence time of the the microwave field on resonance with the atomic tran- atom–resonator-field interaction. The coherence time of sition at the position of the atoms was reduced. This ∼ 150 ns was inferred by comparison of the experimental resulted in a corresponding reduction in the intensity of data with the overlaid sinusoidal function with an am- the spectral features for TCPW = 3.9, 4.1 and 4.3 K in plitude that decays exponentially with a time constant Figs. 4(b-ii) to (b-iv). The reduction in |56si signal as of 150 ns. To increase the Rabi oscillation frequency a TCPW was increased confirms that the atoms were cou- second measurement was made for ∆ = +2 MHz. The re- pled to the microwave field enhanced within the CPW sulting data (filled circles in Fig. 5) exhibit an oscillation resonator. The temperature dependence of the intensity frequency of ∼ 8 MHz and a similar coherence time of of the atomic transition is in good agreement with that 150 ns (continuous curve). From (1) the 3 MHz resonant calculated by considering the coherent evolution of an en- Rabi frequency, (2) the -22.5 dB microwave attenuation semble of atoms with 100-µm-FWHM Gaussian spatial between the source and the NbN chip, (3) the microwave distributions in the x and y dimensions, centered 100 µm field strength in the resonator determined from the data above the resonator center conductor [dashed red curves in Fig. 4(a), and (4) the calculated microwave field dis- in Fig. 4(b)]. In these calculations the power spectrum tribution above the resonator [25], the typical distance of within the resonator was described by a Lorentzian func- the atoms from the chip surface in the experiments was tion with the values of ν3 and Qloaded in Table I. The estimated to be ∼ 100 µm, and the steady-state pop- spatial distribution of the microwave field above the res- ulation of the resonator mode was ∼ 109. Within the onator was determined by finite element methods [25]. coherence time of 150 ns, the Rydberg atoms traveled The coherence time of the atom–resonator-field inter- 300 µm along the resonator. Over this distance the mi- action was determined by driving Rabi oscillations be- crowave field strength and stray electric fields vary. 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