Many-body Landau-Zener transition in cold-atom double-well optical lattices

Qian, Yinyin; Gong, Ming; Zhang, Chuanwei

doi:10.1103/physreva.87.013636

Cited by 12 publications

(10 citation statements)

References 58 publications

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“…In general, it is customary to further approximate the above expression by neglecting the coupling beyond nearest neighbours for both the single-well [10] and double-well lattices [25,28,29]. This is a reasonable assumption for a single-well lattice in the tight-binding regime [14,34], but may not be fully justified in the range of the typical experimental parameters for a double well, as 6 will be discussed later on.…”

Section: Tight-binding Models For Double-well Optical Latticesmentioning

confidence: 99%

“…This is analogous to the nearest-neighbour approximation for the single-well case and is commonly used in the literature [28,29]. Hereinafter, we will refer to the approximate Hamiltonians in (8) and (9) as the (single-particle) full and nearest-neighbour tight-binding models, respectively.…”

Section: Tight-binding Models For Double-well Optical Latticesmentioning

confidence: 99%

“…In this paper, we consider the case of a 1D periodic potential with a double well per unit cell [23][24][25][26][27][28][29], discussing an alternative method for constructing the low-lying generalized MLWFs based on the minimal spread requirement of Marzari and Vanderbilt [21], specifically suited for double-well potentials. In particular, we consider a composite band made of the two lowest Bloch bands and, differently from [21], we design a two-step gauge transformation specific for a composite two-band system which can be solved by integrating a set of ordinary differential equations, with suitable boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials

Modugno

Pettini

2012

New J. Phys.

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We discuss a method for constructing generalized Wannier functions that are maximally localized at the minima of a one-dimensional periodic potential with a double well per unit cell. By following the approach of Marzari and Vanderbilt (1997 Phys. Rev. B 56 12847), we consider a set of band-mixing Wannier functions with minimal spread and design a specific two-step gauge transformation of the Bloch functions for a composite two-band system. This method is suited for efficiently computing the tight-binding coefficients needed for mapping the continuous system to a discrete lattice model. The behaviour of the tight-binding coefficients is analyzed here as a function of the symmetry properties of the double well (including the possibility of parity-breaking), in a range of feasible experimental parameters.

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Section: Tight-binding Models For Double-well Optical Latticesmentioning

confidence: 99%

Section: Tight-binding Models For Double-well Optical Latticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials

Modugno

Pettini

2012

New J. Phys.

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“…It can therefore be viewed as a study of adiabaticity for fields satisfying the Maxwell wave equation and is related to generalizations of the Landau-Zener theory to the many-particle case in condensed matter physics contexts [100][101][102][103][104][105][106][107]. By comparing the effects of successive approximations, such as ignoring the time-dependence of the modes in the diabatic basis and reducing the Maxwell wave equation to an effective Schrödinger equation, we have emphasized some significant differences to the original Landau-Zener problem which is posed in terms of the (true) single-particle Schrödinger wave equation.…”

Section: Discussionmentioning

confidence: 99%

Parametric amplification of light in a cavity with a moving dielectric membrane: Landau-Zener problem for the Maxwell field

Hasan

O’Dell

2016

Phys. Rev. A

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We perform a theoretical investigation into the classical and quantum dynamics of an optical field in a cavity containing a moving membrane ("membrane-in-the-middle" set-up). Our approach is based on the Maxwell wave equation, and complements previous studies based on an effective Hamiltonian. The analysis shows that for slowly moving and weakly reflective membranes the dynamics can be approximated by unitary, first-order-in-time evolution given by an effective Schrödinger-like equation with a Hamiltonian that does not depend on the membrane speed. This approximate theory is the one typically adopted in cavity optomechanics and we develop a criterion for its validity. However, in more general situations the full second-order wave equation predicts light dynamics which do not conserve energy, giving rise to parametric amplification (or reduction) that is forbidden under first order dynamics and can be considered to be the classical counterpart of the dynamical Casimir effect. The case of a membrane moving at constant velocity can be mapped onto the Landau-Zener problem but with additional terms responsible for field amplification. Furthermore, the nature of the adiabatic regime is rather different from the ordinary Schrödinger case, since mode amplitudes need not be constant even when there are no transitions between them. The LandauZener problem for a field is therefore richer than in the standard single-particle case. We use the work-energy theorem applied to the radiation pressure on the membrane as a self-consistency check for our solutions of the wave equation and as a tool to gain an intuitive understanding of energy pumped into/out of the light field by the motion of the membrane.

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“…Despite its simplicity, this model has been applied to a great variety of physical systems, including atomic and molecular systems [5,6], semiconductor superlattices [7], and superconducting devices [8]. In these systems, the two-level LZ model acts as a good starting point to investigate more realistic situations.…”

Section: Introductionmentioning

confidence: 99%

Photon-induced sideband transitions in a many-body Landau-Zener process

et al. 2014

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We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These photon-induced sideband transitions are a signature of the photon-assisted tunneling in our many-body LZ process. In the strong interaction regime, we develop an analytical theory for understanding the sideband transitions, which is confirmed by our numerical simulation. Furthermore, we discuss the quantization of the driving field. In the effective model of the quantized driving field, the sideband transitions can be understood as the LZ transitions between states of different "photon" numbers.

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Many-body Landau-Zener transition in cold-atom double-well optical lattices

Cited by 12 publications

References 58 publications

Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials

Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials

Parametric amplification of light in a cavity with a moving dielectric membrane: Landau-Zener problem for the Maxwell field

Photon-induced sideband transitions in a many-body Landau-Zener process

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