Abstract
Quantum computers have the capability of outperforming their classical counterparts for certain computational problems^{1}. Several scalable quantumcomputing architectures have been proposed. An attractive architecture is a large set of physically independent qubits arranged in three spatial regions where (1) the initialized qubits are stored in a register, (2) two qubits are brought together to realize a gate and (3) the readout of the qubits is carried out^{2,3}. For a neutralatombased architecture, a natural way to connect these regions is to use optical tweezers to move qubits within the system. In this letter we demonstrate the coherent transport of a qubit, encoded on an atom trapped in a submicrometre tweezer, over a distance typical of the separation between atoms in an array of optical traps^{4,5,6}. Furthermore, we transfer a qubit between two tweezers, and show that this manipulation also preserves the coherence of the qubit.
Main
In the quest for an implementation of a quantum computer, scalability is a major concern. In the trappedion approach (see for example ref. 7), a lot of effort is being devoted to building arrays of small ion traps^{8}, and to moving ion qubits whilst avoiding heating and decoherence^{9}. Neutral atoms also offer promising properties for the realization of large quantum registers. For example, one or twodimensional addressable arrays of dipole traps have been demonstrated using holographic techniques^{4}, microfabricated elements^{5}, or active rearrangement of single atoms^{6,10}. An alternative approach is to use the Mott insulator transition to initialize a threedimensional register by loading a Bose–Einstein condensate into an optical lattice^{11}. Recent progress has shown subwavelength addressability in such a system^{12}. To carry out quantum computations, however, an additional key feature is the ability to realize the gate between two arbitrary qubits of the register.
Here we demonstrate a scheme where a neutralatom qubit is transferred between two moving tweezers (‘register’ to ‘moving head’), and then transported towards an interaction zone where the twoqubit gate should be implemented^{13,14,15,16}. We show that these manipulations of the external degrees of freedom preserve the coherence of the qubit, and do not induce any heating. This transport in a moving tweezer is a promising alternative to the recently demonstrated transport of qubits in ‘optical conveyor belts’^{6,17}, or in statedependent moving optical lattices^{18}. Altogether, these results could pave the way towards a scalable neutralatom quantumcomputing architecture.
In our experiment, we trap a single rubidium87 atom in an optical dipole trap created by a tightly focused laser beam^{19,20}. As described in detail in ref. 21, the qubit is encoded onto the 0〉=F=1,M=0〉 and 1〉=F=2,M=0〉 hyperfine ground states separated by ω_{hf}≈6.8 GHz. We initialize the qubit in state 0〉 by optically pumping the atom. We drive singlequbit operations by a Raman transition using two phasedlocked laser beams, one of which is the dipole trap. The internal dephasing time of the qubit, measured by Ramsey interferometry, is approximately 630 μs. This time is mostly limited by the residual motion of the atom in the trap, which leads to a fluctuation of the frequency of the qubit transition. This dephasing can be reversed by applying a spinecho technique, where a πpulse is inserted between the two π/2 pulses of the Ramsey sequence. Using this technique we measure an irreversible dephasing time of 34 ms.
The experimental setup for the moving tweezer is represented in Fig. 1. We reflect the dipoletrap beam off a mirror affixed to a tip–tilt platform before the largenumericalaperture lens. The platform is actuated by piezoelectrical transducers and can rotate with a maximal angle of 2.5 mrad in both the horizontal and vertical directions. We have measured the position of the dipole trap for different angles of the platform by observing the position of the atom on the CCD camera. The maximal angle corresponds to a total displacement of the tweezer of 18±1 μm. This motion is two dimensional, as demonstrated in Fig. 1.
We first analyse the influence of a displacement of the tweezer on the external degrees of freedom of the qubit. For this purpose, we measure the temperature of the single atom in the tweezer using a releaseandrecapture technique^{22} (see the Methods section). In the absence of motion, the temperature of the atom is 56.0±1.4 μK. We repeat this measurement after moving the tweezer by a total distance of 360 μm, consisting of 20 round trips of 18 μm, along the z axis. Each round trip lasts a time of 6 ms. We do not find any measurable loss due to this transport. After the motion, we measure a temperature of 54.8±1.6 μK. As the energy difference between two vibrational quanta in the radial direction is 4 μK, this temperature is compatible with no change on average in the radial vibrational state. This absence of motional heating is a crucial feature for entanglement schemes on the basis of controlled collisions^{16,23} and results from the adiabaticity of the displacement. A motion is adiabatic if the acceleration a fulfils m a σ≪ℏΩ (Ω is the oscillation frequency of the atom, m its mass and σ the extension of the groundstate wavefunction^{24}). This gives a maximum acceleration of ≈10^{4} m s^{−2}, much larger than the experimentally measured ≈15 m s^{−2}.
Second, we study the influence of the motion on the coherence of the qubit. As the duration of the transport is larger than the dephasing time of the qubit (630 μs), we apply the spinecho sequence to rephase the qubit^{21}. The time sequence of the experiment is shown in Fig. 2. Figure 3a shows the amplitude of the spinecho fringes for various trap displacements along the y axis. This amplitude is constant when we scan the tweezer over the whole transverse field of the objective. This demonstrates that the motion does not affect the internal coherence of the qubit. To show the independent twodimensional control of our system, we move the tweezer along the z axis and observe the same behaviour as along the y axis.
We also observe a phase shift of the spinecho fringes, as shown in Fig. 3b. This is evidence that the two states of the qubit dephase with respect to each other during the motion (in a reproducible way), despite the presence of the rephasing πpulse. We attribute this phase shift to the asymmetry of the trajectory during the first and second parts of the roundtrip displacement. We have modelled this effect and found a good agreement with the data (see the Methods section). This understanding of the phase evolution of the qubit during the motion is crucial for a possible implementation in a quantum computer, where qubit phases need to be controlled.
With the idea of transferring an atom from the ‘register’ to the ‘moving head’, we have investigated the transfer of a qubit from one tweezer to a second one. For this experiment, the two traps are superimposed and the positions of both tweezers are fixed. The experimental sequence is shown in Fig. 4a. We load an atom in the first tweezer, transfer it to a second tweezer, and transfer it back to the first tweezer, with no measurable loss. When the two traps have the same depth, we measure a temperature of the atom after the double transfer of 56.3±1.8 μK, whereas the temperature with no transfer is 53.4±1.4 μK. Therefore, the transfer does not induce any significant motional heating.
We analyse the influence of the transfer on the coherence of the qubit by inserting the double transfer between the two π/2pulses of a Ramsey sequence, as shown in Fig. 4a. Figure 4 presents the amplitude and the phase of the Ramsey fringes after this sequence for depths of the second tweezer ranging from 0.2 to 0.6 mK. This transfer does not affect the amplitude of the Ramsey signal when the depth of the second trap is varied, thus showing that the coherence is robust against the transfer between the two traps.
Figure 4c shows that the phase of the Ramsey fringes varies linearly with respect to the depth of the second trap. This is explained by the differential potential experienced by the two states, which is proportional to the depth of the trap U. If the depths of the two traps differ by ΔU, the Ramsey fringes are shifted after a holding time T by a phase proportional to ΔU T/ℏ, with respect to the situation where no transfer is applied. This phase is thus a useful tool to make sure that the two traps are identical.
In conclusion, we have shown that we can move and transfer a single qubit between two tweezers with no measurable motional heating. We have also shown no loss of coherence of the atomic qubit under transfer and displacement. In combination with our holographic array of dipole traps^{4}, and efficient singlequbit operation and readout^{21}, we have made a first step towards designing a scalable architecture of a quantum computer on the basis of neutral atoms.
Methods
Temperature measurement
After trapping a single atom, we switch off the dipole trap for a time adjustable between 1 and ∼30 μs. We then turn the trap back on and check for the presence of the atom. We repeat this sequence 100 times for each release time and calculate the probability of recapturing the atom after the corresponding time of flight. We compare our data with a threedimensional Monte Carlo simulation, taking into account the potential produced by the gaussian trapping beam, and assuming a thermal distribution of the position and the velocity of the atom at the beginning of the time of flight. The error bar of this fitted temperature corresponds to one standard deviation in the leastsquarebased fit.
Phase shift during the motion
The hyperfine splitting of 6.8 GHz means that the dipole trap detuning is slightly larger for 0〉 than for 1〉, giving rise to a small differential lightshift. Therefore, the qubit transition frequency is ω_{hf}+η U/ℏ, with U the depth of the dipole trap and η=7×10^{−4} for our trap. If the tweezer is not moved, the πpulse compensates for the phase accumulated during the two parts of the motion. When the tweezer is moved off axis, the waist of the beam increases slightly, resulting in a shallower trap. Figure 2a shows that with the tweezer starting on axis the atom spends more time far from the axis, where the dipole trap is shallower, whereas on the way back it spends more time around the axis, where the dipole trap is stronger. The average depths are then different for the two parts of the motion, and so are the phases. As the phase of the spinecho signal is the difference of the phases accumulated during the two periods of the motion, it is expected to vary as we move the tweezer further away off axis. We have modelled this effect by calculating the dephasing accumulated during the transport, taking into account the actual displacement of the tweezer from the sensor curve and the measured Rabi frequencies for different positions of the tweezer off axis. The result of this model is shown as circles in Fig. 3b and is consistent with the data.
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Acknowledgements
We would like to thank W. D. Phillips, T. Porto, I. Deutsch and P. Jessen for stimulating discussions. We acknowledge financial support from IFRAF, ARDA/DTO and the European Integrated project SCALA. LCFIO is CNRS UMR8501. M.P.A.J. and A.M.L. are supported by Marie Curie Fellowships. A.G. is supported by a DGA Fellowship.
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Beugnon, J., Tuchendler, C., Marion, H. et al. Twodimensional transport and transfer of a single atomic qubit in optical tweezers. Nature Phys 3, 696–699 (2007). https://doi.org/10.1038/nphys698
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