Atom-by-atom assembly of defect-free one-dimensional cold atom arrays

REPORTS

Cite as: M. Andres et al., Science

10.1126/science.aah3752 (2016).

The detection and manipulation of individual quantum par-

ticles, such as atoms or photons, is now routinely performed

in many quantum physics experiments (1, 2); however, re-

taining the same control in large-scale systems remains an

outstanding challenge. For example, major efforts are cur-

rently aimed at scaling up ion-trap and superconducting

platforms, where high-fidelity quantum computing opera-

tions have been demonstrated in registers consisting of sev-

eral qubits (3, 4). In contrast, ultracold quantum gases

composed of neutral atoms offer inherently large system

sizes. However, arbitrary single atom control is highly de-

manding and its realization is further limited by the slow

evaporative cooling process necessary to reach quantum

degeneracy. Only in recent years has individual particle de-

tection (5, 6) and basic single-spin control (7) been demon-

strated in low entropy optical lattice systems.

Here we demonstrate atom-by-atom assembly of large

defect-free 1D arrays of cold neutral atoms (8, 9).

We use optical microtraps to directly extract individual

atoms from a laser-cooled cloud (10–12) and employ recently

demonstrated trapping techniques (13–16) and single-atom

position control (17–20) to create desired atomic configura-

tions. Central to our approach is the use of single-atom de-

tection and real-time feedback (17, 20) to eliminate the

entropy associated with the probabilistic trap loading (10)

[currently limited to ninety percent loading probability even

with advanced techniques (21–23)]. Related to the funda-

mental concept of “Maxwell’s demon” (8, 9), this method

allows us to rapidly create large defect-free arrays, and

when supplemented with appropriate atom-atom interac-

tions (15, 16, 24–30) provides a potential platform for scala-

ble experiments with individually controlled neutral atoms.

The experimental protocol is illustrated in Fig. 1A. An ar-

ray of 100 tightly focused optical tweezers is loaded from a

laser-cooled cloud. The collisional blockade effect ensures

that each individual tweezer is either empty or occupied by

a single atom (10). A first high-resolution image yields sin-

gle-atom resolved information about the trap occupation,

which we use to identify empty traps and to switch them

off. The remaining occupied traps are rearranged into a

regular, defect-free array and we detect the final atom con-

figuration with a second high-resolution image.

Our implementation relies on fast, real-time control of

the tweezer positions (Fig. 1B), which we achieve by employ-

ing an acousto-optic deflector (AOD) that we drive with a

multi-tone radio-frequency (RF) signal.

This generates an array of deflected beams, each con-

trolled by its own RF-tone (15, 16). The resulting beam array

is then focused into our vacuum chamber and forms an ar-

ray of optical tweezers, each with a Gaussian waist of

900 nm≈

, a wavelength of 809 nm, and a trap depth of

/ 0.9 mK

Uk≈

, Boltzmann constant) that is homoge-

neous across the array within 2% (31).

The tweezer array is loaded from a laser-cooled cloud of

Rubidium-87 atoms in a magneto-optical trap (MOT). After

Atom-by-atom assembly of defect-free one-dimensional

cold atom arrays

Manuel Endres,

1,2

†

Hannes Bernien,

* Alexander Keesling,

* Harry Levine,

* Eric R. Anschuetz,

Alexandre Krajenbrink,

1‡

Crystal Senko,

Vladan Vuletic,

Markus Greiner,

Mikhail D. Lukin

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

Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena,

CA 91125, USA.

Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

*These authors contributed equally to this work.

†

Corresponding author. Email: men[email protected]

‡

Present address: CNRS-Laboratoire de Physique Theorique de l’Ecole Normale Superieure, 24 Rue L’Homond, 75231 Paris Cedex, France.

The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical

science. We use atom-by-atom assembly to implement a platform for the deterministic preparation of

regular one-dimensional arrays of individually controlled cold atoms. In our approach, a measurement and

feedback procedure eliminates the entropy associated with probabilistic trap occupation and results in

defect-free arrays of over 50 atoms in less than 400 milliseconds. The technique is based on fast, real-

time control of 100 optical tweezers, which we use to arrange atoms in desired geometric patterns and to

maintain these configurations by replacing lost atoms with surplus atoms from a reservoir. This bottom-

up approach may enable controlled engineering of scalable many-body systems for quantum information

processing, quantum simulations, and precision measurements.

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the loading procedure, we let the MOT cloud disperse and

we detect the occupation of the tweezers with fluorescence

imaging. Fast, single-shot, single-atom resolved detection

with 20 ms exposure is enabled by a sub-Doppler laser-

cooling configuration that remains active during the re-

mainder of the sequence (31) (see Fig. 2, A to C). Our fluo-

rescence count statistics show that individual traps are

either empty or occupied by a single atom (10, 31), and we

find probabilistically filled arrays with an average single

atom loading probability of

0.6p ≈

(see Figs. 2A and 3A).

The central part of our scheme involves the rearrange-

ment procedure for assembling defect-free arrays (31) (see

Fig. 1A). In the first step, unoccupied traps are switched off

by setting the corresponding RF-amplitudes to zero. In a

second step, all occupied tweezers are moved to the left un-

til they stack up with the original spacing of 2.6 μm. This

movement is generated by sweeping the RF-tones to change

the deflection angles of the AOD and lasts 3 ms (31). Finally,

we detect the resulting atom configuration with a second

high-resolution image. These steps implement a reduction

of entropy via measurement and feedback. The effect is im-

mediately visible in the images shown in Fig. 2, A and B.

The initial filling of our array is probabilistic, whereas the

rearranged configurations show highly ordered atom arrays.

Our approach also allows us to construct flexible atomic

patterns (Fig. 2C).

The rearrangement procedure creates defect-free arrays

with high fidelity. This can be quantified by considering the

improvement of single atom occupation probabilities (Fig.

3A) and the success probabilities, p

, for creating defect-free

arrays of length N (Fig. 3B). The single atom occupation

probability in the left-most forty traps increases from

0.6≈

before rearrangement to 0.988(3) after rearrangement,

demonstrating our ability for high-fidelity single-atom prep-

aration. Furthermore, the success probabilities for creating

defect-free arrays show an exponential improvement. Prior

to rearrangement, the probability of finding a defect-free

array of length N is exponentially suppressed with p

= p

where

0.6p ≈

(blue circles, Fig. 3B). After rearrangement,

we find success probabilities as high as p

= 0.75(1) and p

= 0.53(1) (red circles, Fig. 3B).

The same exponential improvement is observed by con-

sidering the average wait time for producing defect-free ar-

rays, given by T/p

, where T = 200 ms is the cycling time of

our experiment (see Fig. 3B). For example, we are able to

generate defect-free arrays of 50 atoms with an average wait

time of less than 400 ms (red circles, Fig. 3C).

The success probabilities can be further enhanced

through multiple repetitions of the rearrangement protocol.

Figure 4 illustrates the procedure in which we target an

atomic array of fixed length and create a reservoir from sur-

plus atoms in a separate zone. After the initial arrangement

of atoms into the target and reservoir zones, we periodically

take images to identify defects in the target array and pull

atoms from the reservoir to fill in these defects. This en-

hances our initial success probabilities at producing defect-

free arrays within one MOT-loading cycle to nearly the ideal

limit (Fig. 4C).

Finally, a similar procedure can be used for correcting

errors associated with atomic loss. This becomes a signifi-

cant limitation for large arrays because for a given lifetime

of an individual atom in the trap τ, the corresponding life-

time of the N atom array scales as τ/N. To counter this loss,

we repeatedly detect the array occupation after longer time

intervals and replenish lost atoms from the reservoir. This

procedure leads to exponentially enhanced lifetimes of our

arrays (Fig. 4D).

These results demonstrate the ability to generate and

control large, defect-free arrays at a fast repetition rate. The

success probabilities are limited by two factors: the initial

number of loaded atoms and losses during rearrangement.

For example, the average total atom number in our array is

59 ± 5 (31), which results in the cutoff in the success proba-

bility in Fig. 3B starting from

50N ≈

(solid line). For short-

er arrays, the fidelity is mostly limited by losses during

rearrangement. These losses are dominated by our finite

vacuum-limited lifetime, which varies from

6 s≈

12 s≈

(depending on the setting of our atomic dispenser

source), and are only minimally increased by the movement

of the atoms (31). The single atom occupation probability is

correspondingly reduced by a factor exp(–t

/τ), where t

50 ms is the time for the whole rearrangement procedure

(31). This results in the success probabilities of creating

length-N arrays scaling as exp(–t

N/τ), which dominates the

slope for N = 50 in Fig. 3B (dashed line). Currently, we reach

vacuum limited lifetimes only with sub-Doppler cooling ap-

plied throughout the sequence. However, the lifetime with-

out cooling could be improved, for example, by using a

different trapping laser and trapping wavelength (31).

The size of the final arrays can be considerably increased

by implementing a number of realistic experimental im-

provements. For example, the initial loading probability

could be enhanced to 0.9 (21–23) and the vacuum limited

lifetime could be improved to

60 s≈

in an upgraded vac-

uum chamber. Increasing the number of traps in the cur-

rent configuration is difficult because of the AOD

bandwidth of

50 MHz≈

and strong parametric heating in-

troduced when the frequency spacing of neighboring traps

approaches

450 kHz≈

(31). However, implementing two-

dimensional (2D) arrays could provide a path toward realiz-

ing thousands of traps, ultimately limited by the availability

of laser power and the field of view of high-resolution objec-

tives. Such 2D configurations could be realized by either

directly using a 2D-AOD or by creating a static 2D lattice of

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traps [using spatial light modulators (14) or optical lattices

(12)] and sorting atoms with an independent AOD (31). With

increased loading efficiencies (21–23), realistic estimates for

the rearrangement time t

in such 2D arrays indicate that

the robust creation of defect-free arrays of hundreds of at-

oms is feasible (31). Finally, the repetitive interrogation

techniques, in combination with periodic reservoir reload-

ing from a cold atom source (such as a MOT), could be used

to maintain arrays indefinitely.

Atom-by-atom assembly of defect-free arrays forms a

scalable platform with unique possibilities. It combines fea-

tures that are typically associated with ion trapping experi-

ments, such as single-qubit addressability (32, 33) and fast

cycling times, with the flexible optical trapping of neutral

atoms in a scalable fashion. Furthermore, in contrast to sol-

id-state platforms, such atomic arrays are highly homogene-

ous (31) and mostly decoupled from their environment. The

homogeneity of our array should also allow for cooling of

the atomic motion via simultaneous sideband cooling in all

tweezers at once (34, 35).

These features provide an excellent starting point for

multi-qubit experiments, studies of quantum many body

effects and for exploring future applications. The required

interactions between the atoms can be engineered using

several approaches. Even without sideband cooling, exciting

the atoms into high-lying Rydberg states would introduce

strong dipole interactions that can be used for fast entan-

gling gates (24, 25, 27). The parallelism afforded by our flex-

ible atom rearrangement enables efficient diagnostics of

such Rydberg-mediated entanglement. These interactions

may also enable approaches to quantum simulations that

involve both coherent coupling and engineered dissipation

(26, 27), as well as large-scale entangled quantum states for

applications in precision measurements (36).

An alternative approach to engineering interactions in-

volves the integration of atom arrays with nanophotonic

platforms as demonstrated previously (28, 29). These enable

photon-mediated interactions that can be employed to cou-

ple the atoms within a local multi-qubit register or for effi-

cient communication between the registers using a modular

quantum network architecture (3).

Finally, our platform could enable new bottom-up ap-

proaches to studying quantum many-body physics in Hub-

bard models (15, 16, 30), where atomic Mott insulators with

fixed atom number and complex spin patterns could be di-

rectly assembled. This requires atom temperatures close to

the ground state, coherent tunneling between the traps, and

sizable on-site interactions. With side-band cooling, ground

state fractions in excess of 90% have already been demon-

strated (34, 35), and can likely be improved via additional

optical trapping along the longitudinal tweezer axes, which

would also increase on-site interaction strengths. Coherent

tunneling of Rb atoms between similarly sized tweezers has

been observed before by reducing the tweezer distance (15,

16). The parametric heating, currently limiting the minimal

distance between our traps, could be reduced by working

with shallower traps, as needed for tunneling, and by em-

ploying fewer traps to increase the frequency separation

between neighboring traps. Eventually, this approach could

be applied to create ultracold quantum matter composed of

exotic atomic species or complex molecules (37, 38) that are

difficult to cool evaporatively.

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ACKNOWLEDGMENTS

We thank K.-K. Ni, N. Hutzler, A. Mazurenko, and A. Kaufman for insightful

discussion. This work was supported by NSF, CUA, NSSEFF, and Harvard

Quantum Optics Center. H.B. acknowledges support by a Rubicon Grant of the

Netherlands Organization for Scientific Research (NWO). During the completion

of this work, we became aware of a related approach (39).

SUPPLEMENTARY MATERIALS

www.sciencemag.org/cgi/content/full/science.aah3752/DC1

Materials and Methods

Figs. S1 to S5

Movies S1 to S3

References (40, 41)

17 June 2016; accepted 17 October 2016

Published online 3 November 2016

10.1126/science.aah3752

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Fig. 1. Protocol for creating defect-free arrays. (A) A first image identifies

optical microtraps loaded with a single atom, and empty traps are turned off.

The loaded traps are moved to fill in the empty sites and a second image

verifies the success of the operation. (

) The trap array is produced by an

acousto-optic deflector (AOD) and imaged with a 1:1 telescope onto a 0.5 NA

microscope objective, which creates an array of tightly focused optical

tweezers in a vacuum chamber. An identical microscope objective is aligned

to image the same focal plane. A dichroic mirror allows us to view the trap

light on a charge-coupled-device camera (CCD) while simultaneously

detecting the atoms via fluorescence imaging on an electron-multiplied-CCD

camera (EMCCD). The rearrangement protocol is realized through fast

feedback onto the multi-tone radio-frequency (RF) field driving the AOD.

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Fig. 2. Assembly of regular atom arrays.

(

) Single-shot, single-atom resolved fluorescence images

recorded with the EMCCD before (top) and after (bottom) rearrangement. Defects are identified and the

loaded traps are rearranged according to the protocol in Fig. 1, indicated by arrows for a few selected atoms.

(

) Two instances of successfully rearranged arrays (first two pictures), and one instance (last picture) where

a defect is visible after rearrangement. (

) The final arrangement of atoms is flexible, and we generate, e.g.,

clusters of two (top) or ten (bottom) atoms. Non-periodic arrangements and adjustable lattice spacings are

also possible. (

) High-resolution CCD image of trap array. Our default configuration for loading atoms

consists of an array of 100 tweezers with a spacing of 0.49 MHz between the RF-tones, corresponding to a

real-space distance of 2.6 μm between the focused beams (31).

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Fig. 3. Quantifying the rearrangement performance. (A) The initial loading (blue circles) results in an

occupation probability of

0.6≈

for each trap in the array. After rearrangement (red circles), close to unity

filling is reached on the left side of the array. (

) In the initial image, the probability of finding a defect-free

length-N array (starting from the leftmost trap) falls off exponentially with N (blue circles). Following the

rearrangement of all loaded traps to form the largest possible array, we demonstrate strongly enhanced

success probabilities at producing defect-free arrays (red circles). Theory curves show limits set by the

total initial atom number (solid line), the background limited lifetime of τ = 6.2 s (dashed line) and the

product of both (dashed dotted line) (31). (

) Expected amount of time to wait on average to produce a

defect-free array of a given size taking into account the experimental cycle time of 200 ms (150 ms without

rearrangement). Without rearrangement, the wait time grows exponentially (blue circles). Employing the

rearrangement procedure, we can produce arrays of length 50 in less than 400 ms (red circles). All error

bars denote 68% confidence intervals, which are smaller than the marker size in (A) and (B).

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Fig. 4. Creating and maintaining regular arrays using an atomic reservoir. (A) For a given target array

size, surplus atoms are kept in a reservoir and used for repetitive reloading of the array. (

) A 20 atom

target array with a reservoir of atoms on the right. Defects occasionally develop in the target array and are

replaced by atoms in the reservoir. The reservoir depletes as it is used to fill in defects. (

) By performing

repeated rearrangements (once every 50 ms) the probability to successfully produce a defect-free array

in any of these attempts increases and approaches the limit set by the number of initially loaded atoms

(dashed lines). We show data for targeting 40 (purple), 50 (yellow), and 60 (green) atom arrays. Solid

lines are guides to the eye. (

) Probing for defects and filling them once every 100 ms from the reservoir

extends the lifetime of a defect-free array. Shown is the success probability of maintaining arrays of 20

(circles) and 40 (triangles) atoms with (red) and without (blue) replenishing atoms from the reservoir.

With replenishing, the probability to maintain a defect-free array remains at a fixed plateau for as long as

we have surplus atoms in the reservoir. The initial plateau value is set by the probability that no atoms in

the array are lost in 100 ms (calculated value for 10 s single atom lifetime shown as the dotted line). All

error bars denote 68% confidence intervals, which are smaller than the marker size in (C).

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Atom-by-atom assembly of defect-free one-dimensional cold atom arrays

Vladan Vuletic, Markus Greiner and Mikhail D. Lukin

Manuel Endres, Hannes Bernien, Alexander Keesling, Harry Levine, Eric R. Anschuetz, Alexandre Krajenbrink, Crystal Senko,

published online November 3, 2016

ARTICLE TOOLS

http://science.sciencemag.org/content/early/2016/11/02/science.aah3752

MATERIALS

SUPPLEMENTARY

http://science.sciencemag.org/content/suppl/2016/11/04/science.aah3752.DC1

CONTENT

http://science.sciencemag.org/content/sci/354/6315/1021.full

http://science.sciencemag.org/content/sci/354/6315/972.full

REFERENCES

http://science.sciencemag.org/content/early/2016/11/02/science.aah3752#BIBL

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