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Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice

Nature Physics volume 18, pages 259–264 (2022)Cite this article

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Abstract

Discontinuous (first-order) quantum phase transitions and the associated metastability play central roles in diverse areas of physics, ranging from ferromagnetism to the false-vacuum decay in the early Universe1,2; yet, their dynamics are not well understood. Ultracold atoms provide an ideal platform for experimental simulations of quantum phase transitions3,4; so far, however, studies of first-order phase transitions have been limited to systems with weak interactions5,6,7,8, where quantum effects are exponentially suppressed. Here we realize a strongly correlated driven many-body system whose transition can be tuned from continuous to discontinuous. Resonant shaking of a one-dimensional optical lattice hybridizes the two lowest Bloch bands9,10, driving a novel transition from a Mott insulator to a superfluid with a staggered phase order. For weak shaking amplitudes, this transition is discontinuous and the system can remain frozen in a metastable state, whereas for strong shaking, it undergoes a continuous transition towards a superfluid. Our observations of this metastability and hysteresis agree with numerical simulations and pave the way for exploring the crucial role of quantum fluctuations in discontinuous transitions.

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Fig. 1: Schematic of the shaken lattice.
Fig. 2: Simulated phase diagram of the shaken lattice.
Fig. 3: Sweeps across phase transitions and metastability.
Fig. 4: Dynamics of phase transitions.

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Data availability

The data for all figures that support the findings of this study are available in Hierarchical Data Format (HDF5) at the Apollo repository (https://doi.org/10.17863/CAM.78025)

Code availability

The code that supports the plots in this paper is available from the corresponding author upon reasonable request.

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Acknowledgements

This work was partly funded by the European Commission ERC Starting Grant QUASICRYSTAL, the EPSRC Grant EP/R044627/1 and Programme Grant DesOEQ (EP/P009565/1), and by a Simons Investigator Award. We are grateful to E. Gottlob and A. Eckardt for fruitful discussions.

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Authors and Affiliations

  1. Cavendish Laboratory, University of Cambridge, Cambridge, UK

    Bo Song, Shovan Dutta, Shaurya Bhave, Jr-Chiun Yu, Edward Carter, Nigel Cooper & Ulrich Schneider

  2. Department of Physics and Astronomy, University of Florence, Sesto Fiorentino, Italy

    Nigel Cooper

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  1. Bo Song
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Contributions

N.C. and U.S. conceived and supervised the project, with S.D. and B.S. leading the detailed design. B.S., S.B., J.-C.Y. and E.C. performed the experiments. B.S. analysed the experimental data and S.D. performed the numerical simulations. All the authors contributed to the interpretation of the results and writing of the manuscript.

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Correspondence to Ulrich Schneider.

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Extended data

Extended Data Fig. 1 Single-particle correlations.

a, Average correlations \(\langle \langle {\hat{a}}_{i}^{{\dagger} }{\hat{a}}_{i+r}\rangle \rangle\) and \(| \langle \langle {\hat{b}}_{i}^{{\dagger} }{\hat{b}}_{i+r}\rangle \rangle |\) in the ground state with L = 64 sites, fitted with an exponential times a power law. b-c, Correlation length (solid lines) and Luttinger parameter (dashed lines) extracted from the fits across first-order and continuous transitions denoted by vertical lines (cf. Extended Data Fig. 2).

Extended Data Fig. 2 Entanglement and central charge.

a, Von Neumann entanglement entropy across bipartitions of the ground state for L = 64 and \({{{\mathcal{A}}}}=3\) nm with different shaking frequencies, fitted with the conformal field theory (CFT) prediction in Eq. (10). b-f, Fitted central charge c as a function of the shaking frequency at increasing shaking amplitudes, exhibiting discontinuous jumps and smooth peaks characteristic of discontinuous (first-order) and continuous phase transitions, respectively (shown by the vertical dashed lines, with the same color convention as in the phase diagram in Supplementary Fig. S3).

Extended Data Fig. 3 Frequency modulation of lattice laser.

An example of the indirect sweep sequence with a final shaking frequency ff = 21 kHz and a final shaking amplitude \({{{\mathcal{A}}}}=1.9\)nm. a, b and c show variations of the modulation depth Al (the shaking amplitude \({{{\mathcal{A}}}}\)), the shaking frequency f and the laser frequency fl (the displacement of the lattice s), respectively.

Extended Data Fig. 4 Measured band-edge population after different sweep durations for different shaking amplitudes.

a and b show the final population \({{{{\mathcal{N}}}}}_{\pi }\) after direct sweeps in the forward (from a MI to a π-SF state) and backward (from a π-SF to a MI state) directions, respectively. We extract \(\partial {{{{\mathcal{N}}}}}_{\pi }/\partial \tau\) by the linear fits (solid lines). The fit results are shown in Fig. 4c,d.

Extended Data Fig. 5 The band-edge population \({{{{\mathcal{N}}}}}_{\pi }\).

(a) Atom numbers around k = 0 (n0) and k = ± k0 (nπ) are counted inside the boxes in blue and red, respectively. Note that nπ is the sum over the two red boxes. (b-f) are measured with different box sizes lbox/k0 = 0.1, 0.2, 0.4, 0.6, and 0.8, respectively.

Supplementary information

Supplementary Information

Supplementary Sections I–IV and Figs. 1–6.

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Song, B., Dutta, S., Bhave, S. et al. Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice. Nat. Phys. 18, 259–264 (2022). https://doi.org/10.1038/s41567-021-01476-w

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