Control and Entanglement of Individual Rydberg Atoms Near a Nanoscale Device Paloma L. Ocola1Ivana Dimitrova1Brandon Grinkemeyer1Elmer Guardado-Sanchez1 Tamara Ðor devic1Polnop Samutpraphoot1Vladan Vuleti c2and Mikhail D. Lukin1y

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Control and Entanglement of Individual Rydberg Atoms Near a Nanoscale Device

Paloma L. Ocola,1, ∗Ivana Dimitrova,1, ∗Brandon Grinkemeyer,1, ∗Elmer Guardado-Sanchez,1, ∗

Tamara Ðor ¯

devi´

c,1Polnop Samutpraphoot,1Vladan Vuleti´

c,2and Mikhail D. Lukin1, †

1Department of Physics, Harvard University, Cambridge, MA 02138, USA

2Massachusetts Institute of Technology, Cambridge, MA 02139, USA

(Dated: October 25, 2022)

Rydberg atom arrays constitute a promising quantum information platform, where control over several hun-

dred qubits has been demonstrated. Further scaling could signiﬁcantly beneﬁt from coupling to integrated optical

or electronic devices, enabling quantum networking and new control tools, but this integration is challenging

due to Rydberg sensitivity to the electric ﬁeld noise from surfaces. We demonstrate that Rydberg coherence

and two-atom entanglement can be generated and maintained at distances ∼100µmfrom a nanoscale dielec-

tric device. Using coherent manipulation of individual qubits and entanglement-assisted sensing, we map the

spatio-temporal properties of the electric ﬁeld environment, enabling its control and the integration of Rydberg

arrays with micro- and nanoscale devices.

Signiﬁcant progress is currently being made in developing

quantum information processors, promising to tackle compu-

tationally difﬁcult problems. However, further increasing the

computational power may require connecting multiple proces-

sors via quantum interconnects [1]. Rydberg atom arrays have

recently emerged as a leading platform for quantum simula-

tions and quantum information processing, where entangled

states of matter, tests of quantum algorithms and quantum

error correction are currently being explored with hundreds

of qubits [2–4]. While scaling to many thousands of con-

trolled qubits appears feasible [5], signiﬁcant advances can be

achieved by coupling Rydberg arrays to optical, microwave

and electronic devices. Integration with these devices could

enable quantum networking via optical photons [6–9] as well

as novel coupling and control techniques via microwave pho-

tons [10]. In practice, however, Rydberg qubits experience de-

coherence near surfaces caused by ﬂuctuating charges. While

these effects have been studied near various types of dielectric

[11–16] and superconducting [17–21] surfaces, Rydberg atom

integration with such devices remains challenging.

In this Report, we explore the coherence properties of Ry-

dberg atom qubits and entangled states in close proximity to

a silicon nitride (SiN) nanophotonic crystal cavity, used pre-

viously to achieve atom-photon and transportable atom-atom

entanglement [22, 23]. Remarkably, the electric ﬁeld from this

nanoscale device resembles a point-charge of ∼200 single

electron charges (e) with quasi-static ﬂuctuations, enabling

coherent control via decoupling pulse-sequences at distances

as close as 100 µmfrom the device. Moreover, we demon-

strate that certain entangled states are relatively insensitive to

charge noise, allowing us to perform an entanglement-assisted

measurement of the electric ﬁeld environment and study its

control. Together with the recently demonstrated coherent

transport of ground state atoms [23, 24], these observations

open the door for integration of Rydberg arrays with complex

optical, microwave and electronic devices.

∗These authors contributed equally to this work

†To whom correspondence should be addressed; E-mail:

lukin@physics.harvard.edu

Movable

vacuum

system

Objective

SiN device

Silica ber

Optical tweezer

420 nm

1013 nm

Rydberg atoms

1013 nm

420 nm

70S

3/2

1/2

UV diode

FIG. 1. Rydberg atoms near a nanoscale photonic device. (A) A

nanoscale SiN device attached to a tapered ﬁber in a vacuum chamber

is moved relative to a stationary optical tweezer. (B) Measured spec-

tral shift of the |70SiRydberg state as a function of distance from

the device ﬁtted to a point-charge of 126(11) e located on the device

(solid line) that exceeds the Rabi-broadened linewidth (shaded gray

region) for distances <200 µm. (Inset) Spectral shift dependence on

UV power at 160 µm.(C) 420 nm and 1013 nm light used to excite

to the |70SiRydberg state which is shifted by electric ﬁelds.

In our experiments, individual Rubidium-87 atoms are

trapped in optical tweezers and placed at varying distances

from a nanoscale device. The device is suspended on a tapered

silica ﬁber connected to a translation stage (Fig. 1A), allow-

ing it to be positioned 90 −2600µmfrom the trapped atoms.

Each atom is prepared in |gi=|5S1/2, F = 2, mF= 2iand

excited to the |ri=|70S, J = 1/2, mJ= 1/2iRydberg state

via a two-photon transition (Fig. 1C). The excitation beams

arXiv:2210.12879v1 [physics.atom-ph] 23 Oct 2022

t/2 t/2

ππ/2π/2

π/2 π/2

t/4 t/4

ππ/2π/2 π

t/2

FIG. 2. Dependence of single ground-Rydberg qubit coherence

on distance from the device. (A) T∗

2= 200(40) ns measured at

130 µm.(B) T2= 4.1(2) µsmeasured at 130 µm.T2T∗

2implies

that the electric ﬁeld noise is quasi-static. (C) A Carr-Purcell N= 2

decoupling sequence eliminates any decay within the measurement

period, shown for 130 µm.(D) T2(red) and T∗

2(blue) as a function

of distance from the device. T∗

2is limited by electric ﬁeld ﬂuctua-

tions, primarily from the background ﬁeld. T2is limited by thermal

sampling of the spatially-dependent electric ﬁeld. The CP N= 2

sequence eliminates decay at each measured distance and therefore

extends the coherence to be >10 µs(shaded green region). The data

in (A-C) was taken at (dotted line).

are focused onto the atom while the tweezer light is off and

Rydberg population is detected by atom loss. The Rydberg

state experiences a Stark shift ∆ν=1

2α|E|2in an electric

ﬁeld Ewith polarizability α= 534 MHz/(V/cm)2[25]. Its

spectral shift is measured as a function of distance from the

device (Fig. 1B), exceeding the Rabi-broadened linewidth of

3 MHz for |x|<250 µm. The shift follows the electric ﬁeld

scaling of a point-charge (r−4) located on the 31.5µm-long

device (Fig. 1C). Assuming the charge is at the center of the

device gives an estimated charge q=126(11) e [26]. At each

distance the shift is minimized by illuminating the experimen-

tal setup with a UV diode and optimizing its power (Fig. 1B,

inset) [26]. Furthermore, the spectral shift is stable only with

a relatively constant rate of Rydberg excitation, interpreted as

Rydberg-atom ionization creating charges that neutralize the

device surface [26]. The Rydberg spectral shift can be stabi-

lized via both effects as close as 90 µmto the device.

The temporal properties of the electric ﬁeld from the de-

vice are probed by measuring the coherence of the ground-

Rydberg qubit with various control sequences. By pulsing the

420 nm light, we apply a Ramsey sequence π

2−t−π

2to ex-

tract T∗

2as a function of distance from the device (Fig. 2A).

The Ramsey decay is found to be limited by detuning ﬂuc-

tuations of the Rydberg spectral shift caused by the electric

ﬁeld noise. With an echo pulse sequence (Fig. 2B), the co-

herence time is extended by nearly an order of magnitude,

implying that the electric ﬁeld noise is quasi-static. While

ππ

A B C

FIG. 3. Entangled state preparation and lifetime. (A) The Ry-

dberg blockade interaction Ushifts the |rristate and allows for

preparation of the |Wi=1

√2(|gri+|rgi)state which can be

rotated into |Di=1

√2(|gri − |rgi)by applying a differential

phase. (B) Extracted |Wistate ﬁdelity at 170 µm, with population

ρrg,rg +ρgr,gr = 0.87(5) and coherence 2|ρgr,rg |= 0.78(7) with

correction (light purple) [26]. (C) |Wistate lifetime at 160 µmmea-

sured via a π−t−πsequence. (D) The |Wistate lifetime TW,

compared to single-atom T∗

2, is insensitive to common-mode elec-

tric ﬁeld noise and is instead thermally limited.

thermal sampling of the electric ﬁeld gradient limits T2, this

source of decoherence can be further eliminated. Extending

to a Carr-Purcell (CP) N= 2 decoupling sequence (Fig. 2C),

no decay is observed within the 10 µsevolution time at any

measured distance. The scaling of T2and T∗

2with distance

is used to understand the sources of decoherence (Fig. 2D).

Fitting each to a model gives a background ﬁeld standard de-

viation of 0.012 V/cm and bounds the charge ﬂuctuation of

the device to ≤8 e [26].

We next prepare and study entangled atom pairs at var-

ious distances from the device. Two atoms 3.15 µmapart

experience a Rydberg-Rydberg interaction Uin the block-

ade regime where UΩ, with U≈2π×685 MHz and

the single-atom Rabi frequency Ω≈2π×3 MHz. The

atoms are driven with a π-pulse from |ggiinto the sym-

metric state |Wi=1

√2(|gri+|rgi)with a ﬁdelity F=

2(ρrg,rg +ρgr,gr + 2|ρgr,rg |). Characterized following the

method in [27] and corrected for error and loss during prepa-

ration, the resulting ﬁdelity is 0.83(4) (uncorrected 0.70(3))

at 170 µm(Fig. 3B) and 0.87(6) (uncorrected 0.73(3)) at

2.6 mm from the device [26]. This suggests that for the cur-

rent system, the ﬁdelity of the |Wistate is not limited by prox-

imity to the device. Furthermore, the lifetime of the |Wistate

TW, measured through a pulse sequence π−t−πbetween the

|ggiand |Wi(Fig. 3C), is found to be ∼5 times longer than

3.15µm

A B

E F

FIG. 4. Entanglement-assisted sensing of the electric ﬁeld environment. (A) An atom-pair at varying xdistances from the device with

angular orientation θis used to sense the electric ﬁeld gradient via oscillations between |Wiand |Di.(B) The |Wistate lifetime measurement

reveals the gradient-induced oscillations, shown at x=140 µmfor different θ(offset for clarity). The entanglement assists in gradient sensing

for distances where TW> T ∗

2.(C) Angular dependence of the oscillation frequency at different x. Simultaneous ﬁtting of all curves gives

a distance-independent background ﬁeld in x−yand a point-charge on the device. (D) A200 nW UV-power reduction from its optimized

value causes a rotation (53°) of the gradient, measured at x=158 µm.(E) Electric ﬁeld contour plot showing |~

E|as reconstructed from

(C) measurements (black circles) and direction (white arrows). The ﬁber-device junction is set to the origin. (F) Electric ﬁeld contour plot

reconstructed from (D) showing direction at the optimal UV value (gray arrow) and shifted UV value (orange arrow) using the same model

from (C) to extract the changed parameters.

T∗

2(Fig. 3D), indicating that the entangled-state lifetime is not

sensitive to the common-mode electric ﬁeld ﬂuctuations. TW

remains fairly constant over the distances measured (Fig. 3D)

and is likely limited by thermal motion [26].

Given its robustness, the |Wistate can probe the local elec-

tric ﬁeld gradient with greater sensitivity than single-atom

measurements. The gradient creates an energy difference be-

tween |griand |rgiand thus a differential phase, leading

to an oscillation between |Wiand the anti-symmetric state

|Di=1

√2(|gri−|rgi). The oscillation frequency directly

measures the gradient magnitude, observed via a π−t−π

pulse sequence. The direction of maximum gradient is de-

tected by rotating the atom-pair by angle θwith respect to

the x-axis (Fig. 4A). Measured at four distances between

130 µm−192 µm, using a UV power of 400 nW for each,

the gradient maximum occurs at θ∼55° and its magnitude

increases as the atoms approach the device (Fig. 4C). This

differs from the expected 0° gradient orientation for a single

point-charge displaced in x, but can instead be described by

a minimal model that includes a distance-independent back-

ground electric ﬁeld. A combined ﬁt to the data in (Fig. 4C)

reveals a device charge q= 190(10) e and background ﬁeld

E= (Ex, Ey) = (−0.02(1),−0.51(3))V/cm [26]. The os-

cillation frequency follows a point-charge gradient scaling of

r−5along θ= 0° as well as r−3along θ= 90° as predicted

by the model.

Measuring the oscillation between |Wiand |Diat various

angles can be used to study the effect of UV light to under-

stand the behavior illustrated in (Fig. 1C, inset). At 158 µm,

shifting the UV power from the optimal value of 400 nW to

200 nW increases the spectral shift by 6.7 MHz and rotates

the gradient by 53(4)° (Fig. 4D). Assuming the UV power

change modiﬁes the ﬁt parameters q, Ex, Eyfrom Fig. 4C, we

ﬁnd only a signiﬁcant change in the background electric ﬁeld:

∆Ex=−0.21(3) V/cm. A reconstruction of the changed

electric ﬁeld is illustrated in Fig. 4F. However, far from the

device at 4 mm, the electric ﬁeld sensed by the atom does not

vary with UV power. Measuring no change in the spectral

shift for UV powers up to 30 mW, the electric ﬁeld mag-

nitude change can be bounded to <0.05 V/cm [26], much

smaller than the observed |∆Ex|. This indicates that any UV

light effect on the background electric ﬁeld created by the sur-

rounding glass cell is undetectable by the atom for this range

of powers. Additionally, this step in UV power affects the

charge on the device [26].

The inﬂuence of the UV illumination on the present sur-

faces can be understood by reconciling our observations.

First, when choosing the optimal UV power at each distance,

our data (Fig. 1C) agrees with only a point-charge on the de-

vice. This is especially apparent for the measurements at neg-

ative xdistances where the atom is much closer to the ﬁber

than the device and the spectral shift remains near zero [26].

Second, a small deviation from the optimal UV power in-

creases the total electric ﬁeld |E|at close distances but does

not signiﬁcantly change the charge qon the device. There-

fore, the ﬁber surface likely harbors a charge distribution that

creates a background electric ﬁeld when using a UV power

that slightly deviates from the optimal. Remarkably, we can

repeatably stabilize to a conﬁguration where the ﬁber has no

remaining charge by choosing the UV power that minimizes

the spectral shift [26]. This result enables the possibility of

coherent control of Rydberg atoms near such devices and may

also beneﬁt other quantum platforms that are sensitive to sur-

face charges [28].

These observations demonstrate the feasibility of interfac-

ing micro- and nanoscale devices with Rydberg atom arrays.

Potential improvements include using in-vacuum electrodes

for better electric ﬁeld control, minimizing the device size, or

choosing a principal quantum number nto balance the Ry-

dberg interaction strength with electric ﬁeld sensitivity [26].

Importantly, even under present conditions, a Rydberg atom

array placed ∼250 µmaway remains minimally perturbed

by the device. At this distance, a ground-state atom can be

entangled with a photon at the device [22, 29] and coher-

ently transported to an atom array in the same tweezer [24]

as demonstrated from the nanophotonic cavity in [23]. The

transported atom can then be entangled with the Rydberg-

atom quantum processor, opening a quantum optical channel

via teleportation [30] to a photonic state or to a distant quan-

tum processor. Such optical interfaces can also be utilized

for fast, nondestructive readout for quantum error correction

protocols [31, 32]. More broadly, our work motivates inte-

grating Rydberg atom arrays with other devices at this scale.

For example, with properly designed decoupling sequences

and charge stabilization, integration with a mesoscopic super-

conducting interface is possible, enabling the application of

circuit QED techniques and exploration of novel hybrid sys-

tems [10, 33–35].

Acknowledgments: We thank S. Ebadi, T.T. Wang, D. Blu-

vstein, T. Manovitz, G. Semeghini, and S. Evered for useful

discussions, technical assistance, and sharing of laser light.

We also acknowledge M. Greiner, R. Riedinger, and H. R.

Sadeghpour for insightful discussions. Funding: This work

was supported by the Center for Ultracold Atoms, the Na-

tional Science Foundation, AFOSR MURI, DOE QSA Center

and ARL CDQI. B.G. acknowledges support from the DOD

NDSEG. The device was fabricated at the Harvard CNS (NSF

ECCS-1541959). Author contributions: P.L.O., I.D. and

E.G-S. performed the measurements. P.L.O., I.D., B.G., and

E.G-S. analyzed data. B.G. and T.Ð. developed the analyti-

cal coherence models. P.S. and P.L.O. fabricated the device.

All work was supervised by V.V. and M.D.L. All authors dis-

cussed the results and contributed to the manuscript. Com-

peting interests: V.V. and M.D.L. are co-founders and share-

holders of QuEra Computing. Data and materials availabil-

ity: All data needed to evaluate the conclusions in the paper

are present in the paper and the supplementary materials.

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ControlandEntanglementofIndividualRydbergAtomsNearaNanoscaleDevicePalomaL.Ocola,1,IvanaDimitrova,1,BrandonGrinkemeyer,1,ElmerGuardado-Sanchez,1,TamaraÐor¯devi´c,1PolnopSamutpraphoot,1VladanVuleti´c,2andMikhailD.Lukin1,y1DepartmentofPhysics,HarvardUniversity,Cambridge,MA02138,USA2MassachusettsIns...

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Control and Entanglement of Individual Rydberg Atoms Near a Nanoscale Device Paloma L. Ocola1Ivana Dimitrova1Brandon Grinkemeyer1Elmer Guardado-Sanchez1 Tamara Ðor devic1Polnop Samutpraphoot1Vladan Vuleti c2and Mikhail D. Lukin1y

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