Realization of a Fermi-Hubbard Optical Tweezer Array

Spar, Benjamin M.; Guardado-Sanchez, Elmer; Chi, Sungjae; Yan, Zoe; Bakr, Waseem

doi:10.1103/physrevlett.128.223202

Cited by 61 publications

(36 citation statements)

References 42 publications

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“…The ABQMC method can also be straight-forwardly applied to the time-evolution of pure states in either the plane-wave or coordinate many-body bases, which is highly relevant for recent experiments on optical-tweezer arrays. [9][10][11] Our results for the average charge density in the Hubbard model show agreement with numerically exact results in multiple examples, thus validating our implementation. At moderate coupling of the order of half bare bandwidth, we observe that only two imaginary-time slices suffice to obtain excellent results in the temperature range relevant for optical lattice experiments.…”

Section: Introductionsupporting

confidence: 81%

“…Such a setup has been experimentally realized. 10,11,19,22 Replacing e −βH(0) → |ψ(0) ψ(0)| in Eq. ( 20) leads to the expression for the time-dependent expectation value of observable…”

Section: Abqmc Methods For Time-dependent Quantitiesmentioning

confidence: 99%

“…1 Ultrafast pumpprobe spectroscopies can unveil complex excitation and relaxation pathways in strongly correlated materials 2,3 (e.g., the cuprates, transition-metal oxides, and organic salts) and also provide means to manipulate their electronic phases. [4][5][6] Ultracold atoms in optical lattices 7,8 and optical-tweezer arrays [9][10][11] have been used as quantum simulators of paradigmatic models of condensedmatter physics, such as the Hubbard model. 12,13 Recent experiments with ultracold fermionic atoms have probed both equilibrium (e.g., the equation of state, 14 charge and spin correlation functions, [15][16][17] identification of string patterns 18 ) and transport properties (by monitoring charge, 19 mass, 20,21 or spin 22 diffusion) of the twodimensional Hubbard model.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice

Janković¹,

Vučičević²

2022

Preprint

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We devise and benchmark a numerically exact quantum Monte Carlo (QMC) method for interacting electrons on a lattice, that we dub the alternating-basis QMC (ABQMC). The method is uniquely suited to evaluate charge and spin density and the corresponding correlation functions, in both direct and reciprocal space, imaginary or real time. The formalism applies in and out of thermal equillibrium, described by either the canonical or grand-canonical ensemble. The method relies on Suzuki-Trotter decomposition (STD) and owes flexibility to the representation of the kinetic and interaction terms in the many-body bases in which they are diagonal. We formulate a Monte Carlo (MC) update scheme that respects both the momentum and particle-number conservation laws, to restrict the configuration space and thus improve the efficiency of the sampling. To test the method, we perform various calculations for the Hubbard model on finite square lattices of up to 48 sites. We obtain the equation of state (density vs. chemical potential curve) in agreement with reference methods. We also evaluate the (real-time) dynamics of the survival probability of pure densitywave-like states: At small lattice sizes, where the exact diagonalization results are available, we demonstrate the validity of our method at short times; We then proceed to investigate this dynamics on the 4 × 4 Hubbard cluster. Finally, we discuss the extent of the fermionc sign problem and the current limitations of our method, both primarily related to the number of time-slices that we take in the STD.

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Section: Introductionsupporting

confidence: 81%

Section: Abqmc Methods For Time-dependent Quantitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice

Janković¹,

Vučičević²

2022

Preprint

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show abstract

“…The points at 4 and 5 ms are averaged over 6000 and 14,000 repetitions, respectively. complicated many-body states (22,25,26). A complementary approach is to rapidly assemble such states with optical tweezer arrays.…”

mentioning

confidence: 99%

Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice

Young

Eckner

Schine

et al. 2022

Science

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Quantum walks provide a framework for designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. We do this by combining the fast, programmable control provided by optical tweezers with the scalable, homogeneous environment of an optical lattice. With these tools we study continuous-time quantum walks of single atoms on a square lattice and perform proof-of-principle demonstrations of spatial search with these walks. When scaled to more particles, the capabilities demonstrated can be extended to study a variety of problems in quantum information science, including performing more effective versions of spatial search using a larger graph with increased connectivity.

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“…The confinement of fermionic atoms in optical lattices allows the observation of the Mott metal-insulator transition, antiferromagnetic correlations, and spin-charge separation in one-dimensional systems with hundreds of lattice sites [29][30][31][32][33]. Recently, the level of control and flexibility (geometry-lattice) was improved in an eight-site Fermi-Hubbard chain near halffilling achieved with lithium-6 atoms in an optical tweezer array, which allows one more motivation for the present study [34].…”

Section: Introductionmentioning

confidence: 99%

The cumulant Green's functions method for the Hubbard model

Lira¹,

Riseborough²,

Silva–Valencia³

et al. 2022

Preprint

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We study the single-band Hubbard model under the action of an external magnetic field using the cumulant Green's functions method (CGFM). The starting point of the method is to diagonalize a cluster containing N correlated sites ("seed") and employ the cumulants calculated from the cluster solution to obtain the full Green's functions for the lattice. All calculations are done directly, and no self-consistent process is needed. We benchmark the one-dimensional results for the gap, the ground-state energy, and the double occupancy obtained from the CGFM against the corresponding exact results of the thermodynamic Bethe ansatz and the quantum transfer matrix methods. The results for the CGFM tend systematically to the exact one as the cluster size increases. The particlehole symmetry of the density of states is fulfilled. The method can be applied to any parameter space for one, two, or three-dimensional Hubbard Hamiltonians and can also be extended to other strongly correlated models, like the Anderson Hamiltonian, the t − J, Kondo, and Coqblin-Schrieffer models.We also calculate the effects of positive magnetic fields as a function of the chemical potential, and we identify a finite cluster effect (Phase VI) characterized by a partially filled band and negative magnetization (nup < n down ). This phase survives for clusters containing up to N = 8 sites but tends to disappear as the size of the cluster increases. We include a simple application to spintronics, where we used these clusters as correlated quantum dots to realize a single-electron transistor when connected to Hubbard leads. We calculate the phase diagram, including the new cluster phase, using the magnetic field and chemical potential as parameters for N = 7 and N = 8.

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Realization of a Fermi-Hubbard Optical Tweezer Array

Cited by 61 publications

References 42 publications

Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice

Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice

Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice

The cumulant Green's functions method for the Hubbard model

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