Quantum memory with strong and controllable Rydberg-level interactions

Abstract

Realization of distributed quantum systems requires fast generation and long-term storage of quantum states. Ground atomic states enable memories with storage times in the range of a minute, however their relatively weak interactions do not allow fast creation of non-classical collective states. Rydberg atomic systems feature fast preparation of singly excited collective states and their efficient mapping into light, but storage times in these approaches have not yet exceeded a few microseconds. Here we demonstrate a system that combines fast quantum state generation and long-term storage. An initially prepared coherent state of an atomic memory is transformed into a non-classical collective atomic state by Rydberg-level interactions in less than a microsecond. By sheltering the quantum state in the ground atomic levels, the storage time is increased by almost two orders of magnitude. This advance opens a door to a number of quantum protocols for scalable generation and distribution of entanglement.

ARTICLE

Received 8 Jun 2016 | Accepted 19 Oct 2016 | Published 21 Nov 2016

Realization of distributed quantum systems requires fast generation and long-term storage of quantum states. Ground atomic states enable memories with storage times in the range of a minute, however their relatively weak interactions do not allow fast creation of non-classical collective states. Rydberg atomic systems feature fast preparation of singly excited collective states and their efcient mapping into light, but storage times in these approaches have not yet exceeded a few microseconds. Here we demonstrate a system that combines fast quantum state generation and long-term storage. An initially prepared coherent state of an atomic memory is transformed into a non-classical collective atomic state by Rydberg-level interactions in less than a microsecond. By sheltering the quantum state in the ground atomic levels, the storage time is increased by almost two orders of magnitude. This advance opens a door to a number of quantum protocols for scalable generation and distribution of entanglement.

DOI: 10.1038/ncomms13618 OPEN

Quantum memory with strong and controllable

Rydberg-level interactions

Lin Li1 & A. Kuzmich1

1 Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA. Correspondence and requests for materials should be addressed to A.K. (email: mailto:[email protected]

Web End [email protected] ).

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Atomic systems involving highly excited Rydberg states are an attractive system for the continuing quest to realize large-scale quantum networks16. An ultra-cold atomic

ensemble in a quantum superposition of a ground and a Rydberg state features both rapid and deterministic preparation of quantum states and their efcient transfer into single-photon light elds7,8. Notable achievements include the demonstration of deterministic Rydberg single-photon sources9,10, atom-photon entanglement11, many-body Rabi oscillations1215, photon anti-bunching and interaction-induced phase shifts16,17 and single-photon switches1820. In parallel to these efforts, signicant advances have been made in employing Rydberg interactions for entanglement of pairs of neutral atoms2123 and many-body interferometry24.

All these experimental demonstrations relied critically on the strong interactions between Rydberg atoms. The interactions prevent more than one atom from being excited into a Rydberg state within a volume called the blockade sphere, if excitation into the Rydberg state is slow7. In the opposite limit of fast excitation to the Rydberg state, the interactions between the atoms act by dephasing the collective multi-atom states, thereby removing quantum state components with more than one excited atom from the observed Hilbert subspace25. Both Rydberg blockade and dephasing mechanisms contribute to the sub-Poissonian statistics of the output light elds in experiments of refs 9,10,12,16.

However, the large values of the electric dipole transition elements between Rydberg states also translate into a magnied sensitivity of these states to black-body radiation and ambient electric elds, leading to their relatively short lifetimes1,26. Spontaneous emission, atomic motion and collisions further limit storage times for the ground-Rydberg atomic coherence9,18. In contrast, ground atomic states are ideal for preserving quantum coherence27, but implementation of fast and deterministic quantum operations is challenging due to their weak interactions. For example, deterministic single photons can be produced using measurement and feedback of Raman-scattered light elds28, but the generation times are B1 msthree orders of magnitude longer than in Rydberg approaches. Such considerations suggest to employ Rydberg levels for interactions and ground levels for storage to achieve both fast quantum operations and long-lived memory. In this work, we demonstrate a quantum memory where a non-classical polariton state created by Rydberg interactions is sheltered in the ground hyperne sublevels for long-term storage.

ResultsExperimental set-up. Our experimental approach is illustrated in Fig. 1: two 795 nm Raman elds (Op and Oc) are applied to create an approximately coherent state of a spin-wave between the ground hyperne states |ai and |bi in an ultra-cold ensemble of

87Rb. Next, a 297 nm laser pulse O1 couples state |bi directly to

state |ri (np3/2) creating a Rydberg polariton state. Subsequently,

another 297 nm laser pulse O2 transfers the excitation from the Rydberg state into state |bi for storage. After a storage period Tg

in the ground states memory, the read-out eld Or converts the atomic excitation into the retrieved light eld. The latter is directed onto a beam splitter and is subsequently detected by single-photon detectors D1 and D2. Additional details of the experimental protocol are given in Supplementary Notes 1 and 2.

Rydberg excitation. Single-photon excitation from the ground state |bi to the Rydberg state |ri (62p3/2) is studied in Fig. 2. The

normalized sum Sn of the D1 and D2 detection rates is shown in Fig. 2a as a function of single-photon detuning dr from the |bi2|ri resonance. The measured (fwhm) width of the spectrum

g/2p 1.3 MHz is largely determined by the 0.7 ms duration of the

excitation pulse O1. The population of single excitation prepared in |bi, N (at dr 0) is shown in Fig. 2b as a function of Raman

excitation population NR in |bi (no coupling to the Rydberg

state). N and NR are obtained by normalizing the corresponding probabilities of photoelectric detection by the retrieval, transmission and detection efciencies (Supplementary Note 3). The data are t with a function of N zwNR exp( wNR), where

z 0.20(1) and w 0.87(4) are adjustable parameters. The t is

suggested by the dephasing mechanism of multi-particle Rydberg excitations put forward in ref. 25. Here z corresponds to the population transfer efciency of the |bi-|ri-|bi process in

the absence of loss due to multi-particle dephasing, whereas the maximum single excitation preparation efciency (including multi-particle dephasing loss) in state |bi is xm z/e.

The coherence properties of the ground-Rydberg transition are investigated in Fig. 3a by measuring the retrieved signal as a function of storage time Tr in state |62p3/2i. The fast signal decay

(with 1/e lifetime tr 1.58(5) ms) is a result of the atomic

motional dephasing. During the Rydberg excitation, a spin-wave with phase eik1 r is imprinted on the ground-Rydberg coherence by the O1 eld, where k1 is the wave-vector of O1, r is the atomic

D2

a

D1

c r

p

BS

1

y

x z

2

Dipole trap

b

(i) (ii) (iii)

r

|r |r

|r

|e |e |e

|a |a |a

|b |b |b

1 1 2

r

c

p

Figure 1 | Overview of the experiment. (a) Essential elements of the experimental set-up. An ultra-cold 87Rb gas is conned in a crossed dipole trap formed by two 1,064 nm elds. Two 795 nm beams (probe and control) and a 297 nm beam are focused on the atomic sample with waists (op, oc,

o1,2) (5, 25, 18) mm, respectively. The probe and control beam are aligned

with an angle 3, while the 297 beam counter propagates with the probe beam. Probe Op and control Oc laser elds are orthogonally circularly polarized. To avoid the dephasing of Rydberg state induced by inhomogeneous light shifts, the dipole trap is turned off before the Rydberg excitation eld O1 and switched back on after the Rydberg transfer eld O2.

(b) Level diagram and experimental protocol. (i) Atoms are initially prepared in state |ai by means of optical pumping. The atomic ensemble is

driven from |ai to |bi by the probe eld Op and control eld Oc. Next, the

297 nm eld O1 couples |bi directly to the Rydberg state |ri, creating a

singly excited Rydberg state. (ii) By applying the 297 nm eld O2, the

short-lived Rydberg excitation is mapped into the ground state |bi for

storage. (iii) The ground-state excitation is retrieved by the read eld Or and measured at D1 and D2. The atomic levels involved are |ai |5s1/2,

F 1, mF 0i, |bi |5s1/2, F 2, mF 2i, |ei |5p1/2, F 1, mF 1i and

|ri |np3/2, mJ 3/2i.

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13618 ARTICLE

a b

a b

1

0.75

Raman

n =62 n =70

n =29

1.5

1

0.5

0.08

0.06

N

g(2) ()

g(2) ()

S n

0.50

0.04

0.02

0 0

0.25

0 2 1 0 1 1

2 2 3 4 [afii9829]r /2[afii9843] (MHZ)

80 0 80 160

(s)

0 160 80 0 80 160

(s)

0 160 80 0 80 160

(s)

0 160

c d

NR

1.5

1

0.5

Figure 2 | Single-photon excitation to Rydberg p state. (a) Single-photon spectroscopy of |bi2|ri |62p3/2, mJ 3/2i transition. The normalized

photoelectric detection rate Sn of the retrieved eld is shown as a function of detuning (dr). The data are t with a Lorentzian prole. (b) N, the population of prepared single excitation (with O1 and O2 elds ) is shown as a function of Raman excitation population NR. Error bars, 1 s.d.

1.5

1

0.5

g(2) ()

g(2) ()

1.5

1

0.5

0 160 80 0 80 160 (s)

1

0.75

Figure 4 | Quantum statistics. Measured second-order intensity correlation function g(2) as a function of delay t. The data bins for g(2)(0)

are highlighted. (a) g(2)(t) is measured with retrieved coherent light created by the two Raman elds Op and Oc. (bd) 297 nm elds (O1 and O2)

couple state |bi to a Rydberg state |np3/2i, and g(2)(t) is measured at

n 29, 62 and 70, respectively. Error bars, 1 s.d.

a b

S n

0.50

S n

1

0.75

0.50

0.25

0

0.25

0 0 1 25 50

0.5 75 100

0

Tr (s)

Tg (s)

Figure 3 | Temporal dynamics of atomic polariton. (a) The normalized photoelectric detection rate Sn of the retrieved eld is shown as a function of storage time Tr in the Rydberg state. The data are t with a Gaussian function exp( (Tr Td)2/t2r), while Td 1 ms is the delay between two

297 nm elds O1 and O2 for Tr 0 and tr 1.58(5) ms. (b) The normalized

photoelectric detection rate Sn of the retrieved eld is shown as a function of storage time Tg in the ground states coherence. The data are t with function exp( (Tg Td)2/t2g), where Td 6 ms is the delay between

the Raman excitation and the readout for Tg 0 and tg 71(2) ms.

Error bars, 1 s.d.

position and the spin-wave period is Lr 2p/|k1| 297 nm. For a

gas of atoms of mass M at a temperature T, atomic motion smears the spin-wave phase grating and leads to a 1/e decoherence time of trLr= 2p

kBT=M p

(refs 28,29), from which the inferred atom temperature is TC10 mK. A lower value of TC7 mK is found by observing the thermal expansion of the atomic cloud. The difference between the two measurements is a possible indication of atomic heating by the repeated application of the memory protocol. The tr 1.58(5) ms coherence time for the

|62p3/2i state is nearly identical to the tr 1.58(2) ms found for

the |29p3/2i state (Supplementary Note 4), indicating the absence

of Rydberg interaction-induced decoherence.

Ground-state coherence. To achieve longer storage time, we apply the O2 eld to coherently transfer the excitation from the

Rydberg state |ri to the ground state |bi, with the single-photon

detuning dr 0. Due to the non-collinear geometry between the

probe and control elds with respective wave-vectors kp and kc, the atomic excitation forms a ground states spin-wave, with phase eiDk r, where the wave-vector mismatch is Dk kp kc and the

spin-wave period is Lg 2p/|Dk| 15 mm. The stored excitations

can be converted into a propagating eld by applying a read-out

eld Or. To study the temporal dynamics of the quantum memory, the retrieved signal is measured as a function of the storage time Tg in the ground hyperne sublevels, as shown in

Fig. 3b. The observed 1/e quantum memory lifetime is tg

71(2) ms, while the expected lifetime from the scaled value of the ground-Rydberg coherence is tr (Lg/Lr)E80 ms. Assuming

the difference in the two values is due to diffusion of atoms out of the ensemble in the transverse (x and y) dimensions, we estimate the transverse waist (1/e2) of the atomic ensemble to be C6(1) mm, which agrees with the measured 5 mm waist of the probe eld (Supplementary Note 4). In the future, the quantum memory lifetime can be extended into the minute range by employing a suitable state-insensitive optical lattice capable of atom connement on a length scale smaller than the spin-wave period Lg (refs 27,30).

Quantum statistics. To characterize the non-classical behaviour of our quantum memory, the atomic excitation is read out after a storage time of Tg 2 ms and a Hanbury Brown-Twiss

measurement is performed on the retrieved eld with a beam splitter followed by two single-photon detectors D1 and D2. The photoelectric detection events at detectors D1 and D2 are cross correlated, with the resulting second-order intensity correlation function g(2)(t) shown in Fig. 4, where t is the time delay between the detection events. Panel (a) shows the measurement for an approximately coherent state created by the two Raman elds Op and Oc. The measured second-order intensity correlation function at zero delay g(2)(0) 1.06(8) is consistent with unity.

Panels (bd) show the quantum statistics of a memory coupled to Rydberg levels np3/2 for n 29, 62 and 70, respectively.

As a result of the chosen principal quantum numbers (nt70) and sample size (B10 mm) in our experiment, interactions between the most distant Rydberg atom pairs are in the van der Waals regime, which scale as Bn11 (ref. 1). For low values of n, the presence of multiple excitations is expected and the measured g(2)(0) 1.22(14) for n 29 is consistent with unity. When the

interactions are not sufciently strong for the blockade to be operational over the entire ensemble, more than one Rydberg atom can be excited. Van der Waals interactions lead to the accumulation of phase shifts between different atomic pairs,

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g(2)(0)

1

0.75

0.50

0.25

00 10 20 30 40Tg (s)

decoupling them from the phase-matched collective emission mode of the read-out stage. The observed suppression of two-photon events at zero delay for high-lying Rydberg states n 62 and 70 reects Rydberg excitation blockade and

interaction-induced dephasing between multiple excitations and demonstrates the single-photon character of the retrieved eld. The transition from the classical statistics to the manifestly quantum regime is associated with an approximately four orders of magnitude increase in the interaction strength from n 29

to 70. The measured values of g(2)(0) 0.22(8) for n 62

and g(2)(0) 0(0.04) for n 70 conrm the preparation of

single-quanta in the ground memory states. The quantum statistics of the retrieved light eld as a function of storage time are shown in Fig. 5, with all the measured values for g(2)(0) well below unity for up to 42 ms-long storage.

DiscussionWe have demonstrated a quantum memory with 8% efciency to prepare a single excitation in o1 ms, and a memory lifetime of 70 ms. The storage times can be further extended, conceivably up to and beyond several seconds, by adopting a state-insensitive optical lattice27,30. The results presented here show that the two essential quantum network capabilitiesfast quantum state generation and long-term storagecan be achieved at the same time in an atomic-ensemble-based system, opening a route toward a broad range of quantum information protocols. In particular, complex quantum states of atomic ensembles can be generated and stored in their ground states and subsequently converted into highly non-classical states of propagating light elds7.

Methods

Preparation of the ultra-cold atomic sample. To quickly create a dense sample of

87Rb in a low background pressure environment, a 2D magneto-optical trap (MOT) is rst loaded from the background gas. The 3D MOT is then loaded from the cold atomic beam generated by the 2D MOT and directed through a differential pumping opening for 300 ms. For the following 22 ms, the gradient of the 3D

MOT is increased to 25 G/cm to compress and load the atoms into an optical dipole trap formed by two orthogonally polarized YAG laser beams, intersecting at an angle of 22. Sub-Doppler cooling of the atoms is performed by increasing the cooling light detuning and decreasing the power of repumper light for 12 ms. The dipole trap beams have a total power of 5 W and transverse waists of 17 and 34 mm, resulting in a maximum trap depth of C560 mK. The depth of the dipole trap is adiabatically lowered to C30 mK during the 200 ms after the sub-Doppler cooling stage to further cool the atoms, with the atomic temperature of B7 mK inferred from the observed rate of thermal expansion. The peak atomic density is rB2 1011 cm 3. The

atomic ensemble has B10 mm size in the longitudinal (z) dimension, while the B5 mm waist of the focused probe beam determines transverse (x and y )

dimensions of the ensemble. A bias magnetic eld of 3.5 G is switched on and atoms are optically pumped to the 5s1/2, F 1, mF 0 state.

Data acquisition. In each experimental trial, photoelectric events from detectors D1 and D2 are recorded within a time interval of 200 ns, determined by the length

of the retrieved pulse. The photoelectric detection probability for both detectors is given by P P1 P2 N1/N0 N2/N0, where N1,2 are the numbers of detection

events recorded by D1 and D2 and N0 is the number of experimental trails. The probability for detecting double coincidences is given by P12(t) N12(t)/N0, where

N12(t) is the number of coincidences from the two detectors with time delay t. The second-order intensity correlation function is calculated as g(2)(t) P12(t)/(P1P2).

Data availability. The data that support the ndings of this study are available from the corresponding author on request.

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Acknowledgements

We thank P. Berman and M. Saffman for discussions, and P. Zhang for experimental assistance. This work was supported by the Atomic Physics Program and the Quantum

Figure 5 | Non-classical memory dynamics. The single excitation generated with the 70p3/2 state is mapped onto the retrieved eld after being stored in the ground states memory for a time of Tg. The second-order intensity correlation function at zero delay g(2)(0) is measured at different storage times Tg. Error bars, 1 s.d.

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Memories MURI of the US Air Force Ofce of Scientic Research, US Army Research Laboratory and the National Science Foundation.

Author contributions

Both authors contributed substantially to all aspects of this work.

Additional information

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How to cite this article: Li, L. & Kuzmich, A. Quantum memory with strong and controllable Rydberg-level interactions. Nat. Commun. 7, 13618 doi: 10.1038/ncomms13618 (2016).

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