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Quantum register of fermion pairs

Abstract

Quantum control of motion is central for modern atomic clocks1 and interferometers2. It enables protocols to process and distribute quantum information3,4, and allows the probing of entanglement in correlated states of matter5. However, the motional coherence of individual particles can be fragile to maintain, as external degrees of freedom couple strongly to the environment. Systems in nature with robust motional coherence instead often involve pairs of particles, from the electrons in helium, to atom pairs6, molecules7 and Cooper pairs. Here we demonstrate long-lived motional coherence and entanglement of pairs of fermionic atoms in an optical lattice array. The common and relative motion of each pair realize a robust qubit, protected by exchange symmetry. The energy difference between the two motional states is set by the atomic recoil energy, is dependent on only the mass and the lattice wavelength, and is insensitive to the noise of the confining potential. We observe quantum coherence beyond ten seconds. Modulation of the interactions between the atoms provides universal control of the motional qubit. The methods presented here will enable coherently programmable quantum simulators of many-fermion systems8, precision metrology based on atom pairs and molecules9,10 and, by implementing further advances11,12,13, digital quantum computation using fermion pairs14

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Fig. 1: Spatial qubit encoding in a pair of entangled fermions.
Fig. 2: Simultaneous coherent manipulation and parallel readout of hundreds of motional fermion pair qubits.
Fig. 3: Crossover from fermion pair to molecule qubit.
Fig. 4: Second-scale coherence of the fermion pair qubit.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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Acknowledgements

We thank C. Robens for discussions. This work was supported by the NSF through the Center for Ultracold Atoms and Grant PHY-2012110, ONR (grant number N00014-17-1-2257), AFOSR (grant number FA9550-16-1-0324), AFOSR-MURIs on Quantum Phases of Matter (grant number FA9550-14-1-0035) and on Full Quantum State Control at Single Molecule Levels (grant number FA9550-21-1-0069), the Gordon and Betty Moore Foundation through grant GBMF5279, and the Vannevar Bush Faculty Fellowship. M.Z. acknowledges support from the Alexander von Humboldt Foundation.

Author information

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Contributions

The experiment was designed by all authors. T.H., B.O. and N.J. collected and analysed the data. All authors contributed to the manuscript.

Corresponding authors

Correspondence to Thomas Hartke or Martin Zwierlein.

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Extended data figures and tables

Extended Data Fig. 1 Qubit control protocols.

a, Protocol to transfer population between the fermion pair qubit eigenstates at the recoil gap via a Rabi drive of interactions using the magnetic field (Fig. 2 data). b, Protocols for Ramsey measurements of the qubit energy splitting |ΔE| (Fig. 3 data). c, Protocols for measuring coherence at the recoil gap (Fig. 4 data).

Extended Data Fig. 2 Strong driving.

A strongly driven Rabi oscillation at the avoided crossing of Fig. 1c exhibits non-sinusoidal response. The predicted Rabi coupling ΔU/4 = h × 151.98 Hz (see Fig. 2d), which is driven at a modulation frequency of 140.65 Hz, is comparable to the recoil energy gap ER = h × 140.76(3) Hz. The solid line shows a phenomenological guide to the eye composed of three sinusoids with frequencies near ER/h, 2ER/h and 3ER/h.

Source data

Extended Data Fig. 3 Coherence at strong interactions.

The standard deviation of the fermion pair qubit state in an echo sequence with randomized extra phase (standard deviation of \({n}_{|1,1\rangle }\)) quantifies the coherence of the register array at strong interactions. A fitted exponential without offset has 1/e time constant τ = 2.3(1) s at |ΔE| = h × 1.594(7) kHz (orange), τ = 0.84(5) s at |ΔE| = h × 8.98(7) kHz (red) and τ = 0.49(2) s at |ΔE| = h × 50.7(4) kHz (purple), corresponding to magnetic fields B = 206.976(8) G, B = 204.235(8) G and B = 202.091(8) G, respectively. Error bars of τ represent fit error. These data are used in Fig. 4b.

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Hartke, T., Oreg, B., Jia, N. et al. Quantum register of fermion pairs. Nature 601, 537–541 (2022). https://doi.org/10.1038/s41586-021-04205-8

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