Bose-Hubbard model with attractive interactions

Jack, Michael W.; Yamashita, Makoto

doi:10.1103/physreva.71.023610

Cited by 44 publications

(79 citation statements)

References 20 publications

(48 reference statements)

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“…where |N j is the state with all N polaritons on site j [34]. Although the ground state becomes degenerate in the limit κ → −∞, one can generate the W N state with high fidelity since the hopping terms do not induce transitions between the nearly degenerate low energy states.…”

Section: The Phase Transitionmentioning

confidence: 99%

Strongly Interacting Polaritons in Coupled Arrays of Cavities

Hartmann

Brandão

Plenio

2007

2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference

117

179

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The experimental observation of quantum phenomena in strongly correlated many particle systems is difficult because of the short length-and timescales involved. Obtaining at the same time detailed control of individual constituents appears even more challenging and thus to date inhibits employing such systems as quantum computing devices. Substantial progress to overcome these problems has been achieved with cold atoms in optical lattices, where a detailed control of collective properties is feasible but it is very difficult to address and hence control or measure individual sites. Here we show, that polaritons, combined atom and photon excitations, in an array of cavities such as a photonic crystal or coupled toroidal micro-cavities, can form a strongly interacting many body system, where individual particles can be controlled and measured. All individual building blocks of the proposed setting have already been experimentally realised, thus demonstrating the potential of this device as a quantum simulator. With the possibility to create attractive on-site potentials the scheme allows for the creation of highly entangled states and a phase with particles much more delocalised than in superfluids.

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Section: The Phase Transitionmentioning

confidence: 99%

Strongly Interacting Polaritons in Coupled Arrays of Cavities

Hartmann

Brandão

Plenio

2007

2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference

117

179

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“…Jack and Yamashita [205] studied an attractive Bose-Hubbard ring with N = 10 particles in a L = 6 site periodic lattice and argued that by increasing the value of |U/J|, there is a transition from the superfluid regime (see section 4.9) to a soliton regime, occurring approximately at (3.35) (with the corresponding quantum parameters). They identified the soliton state e.g.…”

Section: Quantum Discrete Breathersmentioning

confidence: 99%

“…Buonsante et al [175] used the same model but with up to N = 10 particles in a L = 20 site periodic lattice (at most 10 particles on 12 sites or 5 particles on 20 sites). They argued that the soliton regime in [205] actually could be divided into two regimes: a soliton regime for intermediate |U/J| and a Schrödinger-cat state regime for large |U/J|, where the Schrödinger-cat state is defined as being localized on essentially one site 13 . They also argued that the observables that [205] studied actually indicated a transition, not from the superfluid to soliton regime, but from the soliton to the Schrödinger-cat state regime, but since the system considered in [205] was so small, these transitions occur very close to each other [175].…”

Section: Quantum Discrete Breathersmentioning

confidence: 99%

“…They argued that the soliton regime in [205] actually could be divided into two regimes: a soliton regime for intermediate |U/J| and a Schrödinger-cat state regime for large |U/J|, where the Schrödinger-cat state is defined as being localized on essentially one site 13 . They also argued that the observables that [205] studied actually indicated a transition, not from the superfluid to soliton regime, but from the soliton to the Schrödinger-cat state regime, but since the system considered in [205] was so small, these transitions occur very close to each other [175]. They tested their hypothesis but studying how the different quantities depend on the number of sites, noting that the transition into the Schrödinger-cat regime is independent of the lattice size L and can be estimated with |J/U (N − 1)| ≈ 1/4, while the transition into the soliton regime is size dependent, since the size of the lattice limits how broad a soliton can be, and is approximated with Eq.…”

Section: Quantum Discrete Breathersmentioning

confidence: 99%

“…being a positive integer, which for a delocalized eigenstate should drop as M becomes large while it will remain finite for a state with a significant probability of finding many of the system's particles on one site [175,205]. The dimensionality of the quantum lattice problem, given by Eq.…”

Section: Quantum Discrete Breathersmentioning

confidence: 99%

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Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models : Localization, vortices, and quantum-classical correspondence

Jason¹

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This thesis is mainly concerned with theoretical studies of two types of models: quantum mechanical Bose-Hubbard models and (semi-)classical discrete nonlinear Schrödinger (DNLS) models.Bose-Hubbard models have in the last few decades been widely used to describe Bose-Einstein condensates placed in periodic optical potentials, a hot research topic with promising future applications within quantum computations and quantum simulations. The Bose-Hubbard model, in its simplest form, describes the competition between tunneling of particles between neighboring potential wells ('sites') and their on-site interactions (can be either repulsive or attractive). We will also consider extensions of the basic models, with additional interactions and tunneling processes.While Bose-Hubbard models describe the behavior of a collection of particles in a lattice, the DNLS description is in terms of a classical field on each site. DNLS models can also be applicable for Bose-Einstein condensates in periodic potentials, but in the limit of many bosons per site, where quantum fluctuations are negligible and a description in terms of average values is valid. The particle interactions of the Bose-Hubbard models become nonlinearities in the DNLS models, so that the DNLS model, in its simplest form, describes a competition between on-site nonlinearity and tunneling to neighboring sites. DNLS models are however also applicable for several other physical systems, most notably for nonlinear waveguide arrays, another rapidly evolving research field.The research presented in this thesis can be roughly divided into two parts: 1) We have studied certain families of solutions to the DNLS model. First, we have considered charge flipping vortices in DNLS trimers and hexamers. Vortices represent a rotational flow of energy, and a charge flipping vortex is one where the rotational direction (repeatedly) changes. We have found that charge flipping vortices indeed exist in these systems, and that they belong to continuous families of solutions located between two stationary solutions.Second, we have studied discrete breathers, which are spatially localized and time-periodic solutions, in a DNLS models with the geometry of a ring coupled to an additional, central site. We found under which parameter values these solutions exist, and also studied the properties of their continuous solution families. We found that these families undergo different bifurcations, and that, for example, the discrete breathers which have a peak on one and two (neighboring) sites, respectively, belong to the same family below a critical value of the ring-to-centralv vi site coupling, but to separate families for values above it.2) Since Bose-Hubbard models can be approximated with DNLS models in the limit of a large number of bosons per site, we studied signatures of certain classical solutions and structures of DNLS models in the corresponding Bose-Hubbard models.These studies have partly focused on quantum lattice compactons. The corresponding classical lattice compac...

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Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics

Schlosshauer

2006

Annals of Physics

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We analyze three important experimental domains (SQUIDs, molecular interferometry, and BoseEinstein condensation) as well as quantum-biophysical studies of the neuronal apparatus to argue that (i) the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far; (ii) all observed "restrictions" can be correctly and completely accounted for by taking into account environmental decoherence effects; (iii) no positive experimental evidence exists for physical state-vector collapse; (iv) the perception of single "outcomes" is likely to be explainable through decoherence effects in the neuronal apparatus. We also discuss recent progress in the understanding of the emergence of quantum probabilities and the objectification of observables. We conclude that it is not only viable, but moreover compelling to regard a minimal no-collapse quantum theory as a leading candidate for a physically motivated and empirically consistent interpretation of quantum mechanics.

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Bose-Hubbard model with attractive interactions

Cited by 44 publications

References 20 publications

Strongly Interacting Polaritons in Coupled Arrays of Cavities

Strongly Interacting Polaritons in Coupled Arrays of Cavities

Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models : Localization, vortices, and quantum-classical correspondence

Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics

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