Quantum State Engineering of a Hubbard System with Ultracold Fermions

Christie S. Chiu, Geoffrey Ji, Anton Mazurenko, Daniel Greif, and Markus Greiner

Phys. Rev. Lett. 120, 243201 – Published 14 June 2018

Abstract

Accessing new regimes in quantum simulation requires the development of new techniques for quantum state preparation. We demonstrate the quantum state engineering of a strongly correlated many-body state of the two-component repulsive Fermi-Hubbard model on a square lattice. Our scheme makes use of an ultralow entropy doublon band insulator created through entropy redistribution. After isolating the band insulator, we change the underlying potential to expand it into a half-filled system. The final many-body state realized shows strong antiferromagnetic correlations and a temperature below the exchange energy. We observe an increase in entropy, which we find is likely caused by the many-body physics in the last step of the scheme. This technique is promising for low-temperature studies of cold-atom-based lattice models.

Received 15 December 2017
Revised 10 April 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.243201

Physics Subject Headings (PhySH)

Atom & ion cooling Coherent control Cold gases in optical lattices

Fermi gases Quantum spin models Ultracold gases

Optical microscopy Optical tweezers

Atomic, Molecular & Optical

Authors & Affiliations

Christie S. Chiu, Geoffrey Ji, Anton Mazurenko, Daniel Greif, and Markus Greiner^*

Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

^*greiner@physics.harvard.edu

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Vol. 120, Iss. 24 — 15 June 2018

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Images

Figure 1
Illustration of the quantum state engineering scheme. (Top row) A low-density metallic state removes entropy from a band insulator (BI), after which the two states can be isolated thermally. The BI can then be ramped into an antiferromagnetic (AFM) state by increasing the number of available sites. (Middle row) Map of density inhomogeneity and states in our experimental setup. (Bottom row) We implement our scheme by engineering optical potential landscapes to change the Hamiltonian at each step (see main text and [32]).
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Figure 2
Ultralow entropy BI at $U / t = 7.7 (3)$ . (a) Raw fluorescence image of a single BI, an optical potential schematic, and an average density map of 50 BI realizations. Through entropy redistribution, we create a BI with $> 130$ sites and an average entropy per particle $0.016 (3) k_{B}$ . Error bars denote the standard error of 50 measurements and azimuthal averaging. (b) By continuously tuning the optical potential between a harmonic trap and our entropy redistribution pattern at a constant BI size at $U / t = 5.9 (2)$ , we see a decrease in BI entropy due to an increased entropy redistribution efficiency. The final pattern yields a slightly higher entropy than the optimum, but it is necessary for our scheme. Error bars denote a standard error of $> 20$ measurements each with 133 lattice sites.
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Figure 3
(a) Average density map (40 realizations) and configuration of entropy redistribution at $U / t = 5.9 (2)$ after isolation. Imperfections in the optical potential manifest as singly-occupied sites, as seen at the upper edge of the box. (b) Average density map of 41 images after a ramp highlighting how the insulating wall separates the inner and outer regions, with initialization via a disk pattern. (c) Corresponding density and nearest-neighbor correlator profiles vs radius after ramp. The nearest-neighbor correlations are antiferromagnetic with a strength of up to $C_{1} = - 0.21 (1)$ . A simultaneous fit to both profiles (solid line) gives a temperature of $k_{B} T / t = 0.46 (2)$ . The fit is limited to radius 9, to avoid effects from the insulating wall. Error bars denote a standard error of $> 40$ sets of correlation maps and azimuthal averaging. For $(b) + (c)$ , $U / t = 7.7 (3)$ .
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Figure 4
Examining the final ramp adiabaticity at $U / t = 5.9 (3)$ . (a) A round trip measurement, beginning with an isolated box of doublons surrounded by holes, demonstrates nonadiabaticity, predominantly in the second half of the offset ramp off (circles). Adiabaticity is not significantly improved by initializing the holes and doublons in stripes (diamonds). Horizontal lines with shading indicate reference measurements and uncertainty, taken with no ramp. Lower panels show schematic images for the particle density $n$ and measured average singles density maps for the box (left) and stripe (right) configurations at different times throughout the round-trip ramp. Dashed lines indicate the wall inner edge, while dotted lines enclose BI regions. Error bars are smaller than the markers, and denote a standard error of 40 (187) measurements for the box (stripe) pattern. (b) We quantify heating rates at various points throughout the ramp (upper left), which enable us to approximate the contribution of the entropy increase due to heating. Error bars for entropy measurements (right) denote a standard error of 5 measurements; error bars for heating rates (lower left) are from the fits.
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