Engineering interactions and anyon statistics by multicolor lattice-depth modulations

Cardarelli, Lorenzo; Greschner, Sebastian; Santos, Luís

doi:10.1103/physreva.94.023615

Cited by 47 publications

(64 citation statements)

References 59 publications

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“…In our case this amounts to The ratio U/V depends on the properties of the atomic species and might be controlled externally by means of Feshbach resonances [98] or lattice modulation techniques [103]. A reasonable first approximation is to set U = V , while here we will allow V to vary between 0 < V /J < 1.…”

Section: G Stability Of Vortex Lattices In Systems With a Synthetic mentioning

confidence: 99%

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

et al. 2016

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We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

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Section: G Stability Of Vortex Lattices In Systems With a Synthetic mentioning

confidence: 99%

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

et al. 2016

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“…In this paper we have investigated the correlation functions of a 1D two-component system of anyons with strong repulsive contact interactions. This model is the anyonic generalization of the Gaudin-Yang model and can also be understood as the continuum limit of the two-component anyonic Hubbard model (2AHM) [87,88]. We have derived determinant representations for the temperature-, time-, and space-dependent correlation functions which can be straightforwardly implemented numerically.…”

Section: Discussionmentioning

confidence: 99%

“…The tails of the momentum distribution exhibit the universal 1/k 4 behavior with the amplitude given by Tan's contact which is a monotonic function of the statistics parameter. The natural extension of our work is the consideration of the equivalent lattice system, the 2AHM [87,88], in the strong repulsive limit. In the fermionic case, the well known Hubbard model, the determinant representation of the correlators is already known [139,140] and the long distance asymptotics of the static correlators has also been determined [141].…”

Section: Discussionmentioning

confidence: 99%

“…In this paper we investigate the correlation functions of a 1D two-component system with repulsive contact interactions which can be understood as the anyonic generalization of the Gaudin-Yang model. The literature on 1D anyonic models has been growing steadily in the last years spurred by several experimental proposals of realizing such systems with ultracold atoms in optical lattices using Raman-assisted tunneling [84,85], periodically driven lattices [86] or multicolor lattice-depth modulation [87,88]. Much of the attention was focused on single component systems like the anyonic Lieb-Liniger model [89][90][91] for which we know the ground state characterization [90,92], asymptotic behavior of the correlation functions for homogeneous [26,27,59,[93][94][95] and trapped systems [96,97], entanglement [98,99], and nonequilibrium [100][101][102] properties.…”

Section: Introductionmentioning

confidence: 99%

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Correlation functions of one-dimensional strongly interacting two-component gases

Pâţu¹

2019

Phys. Rev. A

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We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in appropriate limits reduces to the Gaudin-Yang model or the spinor Bose gas. In the case of impenetrable particles we derive a Fredholm determinant representation for the temperature-, time-, and space-dependent correlation functions which is very easy to implement numerically and constitute the starting point for the analytical investigation of the asymptotics. Making use of this determinant representation and the solution of an associated Riemann-Hilbert problem we derive the low-energy asymptotics of the correlators in the spin-incoherent regime characterized by near ground-state charge degrees of freedom but a highly thermally disordered spin sector. The asymptotics present features reminiscent of spin-charge separation with the spin part exponentially decaying in space separation and oscillating with a period proportional to the statistics parameter while the charge part presents scaling with anomalous exponents which cannot be described by any unitary conformal field theory. The momentum distribution and the Fourier transform of the dynamical Green's function are asymmetrical for arbitrary statistics, a direct consequence of the broken space-reversal symmetry. Due to the exponential decay the momentum distribution n(k) at zero temperature does not present algebraic singularities but the tails obey the universal decay lim k→±∞ n(k) ∼ C/k 4 with the amplitude C given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.

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“…The generated low-frequency sidebands of these optical fields can form or break pairs of atoms, and the number of doubly occupied sites has generally been the probed signal. Periodical shaking or modulation of the lattice has also been proposed and used for engineering interesting lattice models [21][22][23][24][25][26], a con-FIG. 1.…”

Section: Introductionmentioning

confidence: 99%

Manipulating multimer propagation using lattice modulation

Dhar

Kinnunen

2019

Phys. Rev. A

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We propose a scheme for controlling the movement of dimers, trimers, and other multimers in optical lattices by modulating the lattice potential. In deep optical lattices the propagation of deeply bound atomic clusters is slowed down by the high energy cost of virtual intermediate states.Adapting the well-known method of lattice modulation spectroscopy, the movement of the clusters can be made resonant by utilizing sequences of bound-bound transitions. Using the scheme, the mobility of each specific cluster can be selectively controlled by tuning the modulation frequency. We formulate a simple and intuitive model and confirm the validity of the model by numerical simulations of dimers and trimers in a one-dimensional optical lattice. arXiv:1902.09428v1 [cond-mat.quant-gas]

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Engineering interactions and anyon statistics by multicolor lattice-depth modulations

Cited by 47 publications

References 59 publications

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

Correlation functions of one-dimensional strongly interacting two-component gases

Manipulating multimer propagation using lattice modulation

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