Quantum-Mechanical Amplification and Frequency Conversion with a Trilinear Hamiltonian

Walls, D. F.; Barakat, Richard

doi:10.1103/physreva.1.446

Cited by 205 publications

(133 citation statements)

References 18 publications

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“…Each eigenstate of the system (17) can be represented by an m th order polynomial with coefficients ρ j (j = 1, 2, ..m.). For a particular energy, we can then construct an ODE for G(u) such that the polynomial coefficients must satisfy the recursion relations of (20). Below we outline the details of this construction.…”

Section: Bethe Ansatz Solution and Mapping To A Schrödinger Equationmentioning

confidence: 99%

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Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

et al. 2007

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We study a three-mode Hamiltonian modelling a heteronuclear molecular BoseEinstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode. Beginning with a semi-classical analogue of the model, we conduct an analysis to determine the phase space fixed points of the system. Bifurcations of the fixed points naturally separate the coupling parameter space into different regions. Two distinct scenarios are found, dependent on whether the imbalance between the number operators for the atomic modes is zero or non-zero. This result suggests the ground-state properties of the model exhibit an unusual sensitivity on the atomic imbalance. We then test this finding for the quantum mechanical model. Specifically we use Bethe ansatz methods, ground-state expectation values, the character of the quantum dynamics, and ground-state wavefunction overlaps to clarify the nature of the ground-state phases. The character of the transition is smoothed due to quantum fluctuations, but we may nonetheless identify the emergence of a quantum phase boundary in the limit of zero atomic imbalance.

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Section: Bethe Ansatz Solution and Mapping To A Schrödinger Equationmentioning

confidence: 99%

“…We remark that in the limit U aa = U bb = U cc = U ab = U ac = U bc = 0, equation (1) is the Hamiltonian studied in [20,21] in the context of quantum optics. In the latter stages of the manuscript we will study this limiting case in some detail.…”

Section: The Modelmentioning

confidence: 99%

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

et al. 2007

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“…The Fock state |1, 1 is thus equivalent to the symmetric state (|e, g + |g, e )/ √ 2. The Hamiltonian that describes the interaction between the two atoms and the field mode will have the form [15,19,20]…”

Section: Example Of Hong-ou-mandel Interference In the Dicke Modelmentioning

confidence: 99%

Interference of composite bosons

Brougham

Barnett

Jex

2010

Journal of Modern Optics

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We investigate multi-boson interference. A Hamiltonian is presented that treats pairs of bosons as a single composite boson. This Hamiltonian allows two pairs of bosons to interact as if they were two single composite bosons. We show that this leads to the composite bosons exhibiting novel interference effects such as Hong-Ou-Mandel interference. We then investigate generalizations of the formalism to the case of interference between two general composite bosons. Finally, we show how one can realize interference between composite bosons in the two atom Dicke model. keywords: interference of bosons, quantum optics, Hong-Ou-Mandel effect.

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“…(4). The above relation (5) corresponding matrix was solved numerically by can also be represented by the equivalent expression Walls and Barakat [16].…”

Section: =0mentioning

confidence: 99%

Relation between quantum statistics of phonons and scattered light

Shumovsky

Tanatar

1993

Physics Letters A

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The resonance model ofthe Raman process with the generation ofa Stokes component is solved exactly. The asymptotic behavior ofthe solution is discussed. Mandel's Q-factor is calculated as a function oftime both for the Stokes and the Rayleigh components fortheir dependence on the quantum statistical properties of the vibration mode (phonons). A qualitative difference between the cases of uncorrelated and correlated phonons is found whichmay have interesting experimentalimplications.

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Quantum-Mechanical Amplification and Frequency Conversion with a Trilinear Hamiltonian

Cited by 205 publications

References 18 publications

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

Interference of composite bosons

Relation between quantum statistics of phonons and scattered light

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