Proposal for a long-lived quantum memory using matter-wave optics with Bose-Einstein condensates in microgravity Elisa Da Rosx1Simon Kanthakx1Erhan Sa glamy urek2 3Mustafa G undo gan1yand Markus Krutzik1 4z

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Proposal for a long-lived quantum memory using matter-wave optics with

Bose-Einstein condensates in microgravity

Elisa Da Ros§,1Simon Kanthak§,1Erhan Sa˘glamy¨urek,2, 3, ∗Mustafa G¨undo˘gan,1, †and Markus Krutzik1, 4, ‡

1Institut f¨ur Physik and IRIS, Humboldt-Universit¨at zu Berlin, Newtonstr. 15, Berlin 12489, Germany

2Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada

3Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada

4Ferdinand-Braun-Institut (FBH), Gustav-Kirchoﬀ-Str.4, 12489 Berlin

Bose-Einstein condensates are a promising platform for optical quantum memories, but suﬀer

from several decoherence mechanisms, leading to short memory lifetimes. While some of these deco-

herence eﬀects can be mitigated by conventional methods, density dependent atom-atom collisions

ultimately set the upper limit of quantum memory lifetime to s-timescales in trapped Bose-Einstein

condensates. We propose a new quantum memory technique that utilizes microgravity as a resource

to minimize such density-dependent eﬀects. We show that by using optical atom lenses to colli-

mate and refocus the freely expanding atomic ensembles, in an ideal environment, the expected

memory lifetime is only limited by the quality of the background vacuum. We anticipate that this

method can be experimentally demonstrated in Earth-bound microgravity platforms or space mis-

sions, eventually leading to storage times of minutes and unprecedented time-bandwidth products

of 1010.

Optical quantum memories (QMs) are devices that can

faithfully and reversibly store and recall the quantum

states of light. They are required in many applications in

quantum information science such as long-distance quan-

tum communications [1, 2], deterministic generation of

multiphoton states [3] and quantum computation [4]. A

recent idea is to deploy QMs in space in order to enable

globe-spanning quantum networks [5–8], ultra-long base-

line Bell experiments [9–12] and probing the interplay be-

tween gravity and quantum physics [13] for which a stor-

age time, τmem, of around ∼1 s is needed. Several atomic

systems have been proven useful for such reversible map-

ping between light and matter qubits. These include

single defects in diamond [14–16], rare-earth ion doped

crystals [17–19], trapped ions [20–22], single trapped

atoms [23, 24], and warm [25–28] and cold [29–33] atomic

gases. Among these platforms, cold-atomic gases have

recently been deployed in space for a number of experi-

ments: optical atomic clocks [34]; the ﬁrst Bose-Einstein

condensate (BEC) on board a sounding rocket [35] and

the International Space Station (ISS) [36]. In addition

to these, missions using cold atoms in space are be-

ing envisioned [37] for gravity and dark matter explo-

ration [38, 39], and currently in development for ultra-

cold atom research including atom interferometry [40]

and advanced atomic clocks on board the ISS [41]. Cold

atom based QMs would share the same technical infras-

tructure with these experiments.

A BEC platform has unique advantages over cold

atoms (obeying a thermal distribution) for optical QMs

due to the inhibition of thermal motion (allowing long

memory lifetime) and its high atomic density (leading

to eﬃcient operation). However, condensates are still af-

fected by several decoherence mechanisms. Among these,

decoherence due to magnetic ﬁeld inhomogeneities [29,

33] can be mitigated by employing rephasing protocols

based on dynamical decoupling [42] and those caused by

AC Stark shifts that are due to inhomogeneous optical

trapping beams can be prevented by employing magic

wavelength techniques [43, 44]. On the other hand, losses

due to atom-atom collisions are usually not reversible,

and cannot be mitigated by such measures. The colli-

sions of cold atoms with the background gas (i.e. 1-body

collisions) can be controlled only with the vacuum qual-

ity, while the collision rates between 2 or 3 atoms within

the cold ensemble (i.e. 2-body and 3-body collision) in-

crease with increasing atom density. These processes be-

come relevant beyond storage times of ∼1 ms. However,

a maximum storage time of around ∼1 s has been ob-

served with bright pulses in a Sodium BEC by tuning the

atom-atom collision cross sections via external magnetic

ﬁelds [45].

In this work, we propose a novel quantum storage

scheme that exploits matter-wave optics to tune the den-

sity of the atomic ensemble to minimize the eﬀects of

density-dependent collisions. This is achieved by letting

the condensate expand after writing the quantum state

of incoming photons into an internal state of the atoms in

the condensate, which is followed by employing the delta

kick collimation (DKC) technique [46–49], ﬁrst to colli-

mate and then to refocus the BEC for eﬃcient read-out

of the stored excitation. This protocol is carried out in a

microgravity environment, which prevents the fall of the

centre of mass without the need for any types of inhomo-

geneous ﬁeld to levitate the atoms. We show that this

technique would allow storage times that are orders of

magnitude beyond what is possible in ground-based ex-

periments and, in fact, only limited by the quality of the

background vacuum. We expect our protocol to reach

a few minutes of storage time with the state-of-the-art

background vacuum values [50, 51].

We assume a pure BEC initially trapped in an optical

arXiv:2210.13859v1 [physics.atom-ph] 25 Oct 2022

BEC

atom

lens

atom

lens

(a)

(b)

FIG. 1. Protocol for a long-lived quantum memory utilizing interaction-driven expansion and delta-kick collimation (DKC)

of a Bose-Einstein condensate (BEC) in microgravity. a) Λ-type three-level structure together with the employed light ﬁelds

during b) diﬀerent stages of the size evolution of the BEC. The quantum state of single photon pulses is imprinted into an

internal excitation of a BEC shortly after its release from an optical dipole trap (ODT). Brief exposure of the BEC by two

consecutive optical lensing potentials allows to stop and subsequently revert the interaction-driven expansion via DKC. This

protocol allows for transition between the complementary density regimes needed for an eﬃcient write-in and read-out of the

memory at high optical depths (ODs) and large coherence times for long-time storage at low atomic densities, respectively.

dipole trap (ODT), as illustrated in Fig. 1. To circumvent

decoherence due to AC-Stark shifts, the quantum state

of single photon pulses is imprinted within the BEC only

shortly after its release from the trap. Timing of the write

pulse is set to mode-match the light intensity and atomic

density distributions with negligible reduction in optical

depth (OD). During free expansion, the internal energy

is converted into kinetic energy, yielding a reduction in

the density and therefore in the 2-body collisions. After

a set time T0, the BEC is exposed to a tailored, optical

potential for a short duration of τDKC. This way, the

BEC experiences a delta-kick, which acts as an optical

atom lens [48, 52–54], resulting in a narrow momentum

distribution. After a chosen collimation time TC, a sec-

ond DKC pulse is applied to refocus the ensemble. At

this point (TC+ 2 T0) it is possible to faithfully recall

the stored quantum information at the original higher

OD. Our protocol thus allows to transition between the

complementary density regimes needed for an eﬃcient

write-in and read-out at high ODs and coherent stor-

age in a dilute quantum gas by exploiting the mean-ﬁeld

driven expansion of a self-interacting BEC. Given by the

point-like source characteristics and single-mode proper-

ties of the BEC, the dispersion of the ensemble can be

shaped after release from the trapping potential by DKC

to nearly stop and ﬁnally revert the expansion.

The quantum memory itself is based on a Λ-type three-

level system as represented in Fig. 1. The states |giand

|sirepresent the ground states of the hyperﬁne structure

of the 87Rb D1line, |52S1/2, F = 1iand |52S1/2, F = 2i,

respectively, while |eiis the excited state |52P1/2, F = 1i.

Collinear probe and control beams address the |gi ←→

|eiand |si ←→ |eitransitions, respectively. The use of

collinear beams [55] ensures both the optimal spin storage

and phase-matching condition which in turn eliminates

decoherence due to recoil collisions [33].

Although ensemble-based memories generally follow

similar considerations [56], we choose to incorporate the

Autler–Townes splitting (ATS) method [33, 57] into our

approach as it requires lower OD and control power for

eﬃcient storage of broadband pulses compared to other

memory protocols implemented in cold-atom systems,

such as electromagnetically induced transparency [58],

which makes it more attractive for applications in quan-

tum information science. Furthermore, lower requisites

on these properties make the ATS protocol more robust

against four-wave mixing noise [33], which is another im-

portant feature for practical applications.

We predict the dynamics of the BEC through a vari-

ational ansatz to numerically solve the time-dependent

Gross–Pitaevskii equation

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Proposalforalong-livedquantummemoryusingmatter-waveopticswithBose-EinsteincondensatesinmicrogravityElisaDaRosx,1SimonKanthakx,1ErhanSaglamyurek,2,3,MustafaGundogan,1,yandMarkusKrutzik1,4,z1InstitutfurPhysikandIRIS,Humboldt-UniversitatzuBerlin,Newtonstr.15,Berlin12489,Germany2DepartmentofPhysi...

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Proposal for a long-lived quantum memory using matter-wave optics with Bose-Einstein condensates in microgravity Elisa Da Rosx1Simon Kanthakx1Erhan Sa glamy urek2 3Mustafa G undo gan1yand Markus Krutzik1 4z

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