Quantum-Optical States in Finite-Dimensional Hilbert Space. II. State Generation

Leoński, W.; Miranowicz, Adam

doi:10.1002/0471231479.ch4

Cited by 30 publications

(37 citation statements)

References 34 publications

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“…To validate our analytical results we can also perform numerical calculations to find the probability amplitudes using the method described in [17]. Thus, we construct the unitary evolution operatorÛ = exp −iĤt using Hamiltonian (1) and apply it to the initial system state |ψ(t = 0) .…”

Section: The Model and Solutionsmentioning

confidence: 97%

“…Therefore, one could expect that with increasing number of photons the Fock states will be involved in the system dynamics. However, the assumption of the weak external pumping and constant amplitudes of the couplings enables us to use the method of the non-linear quantum scissors extensively discussed in [3,17]. In consequence, we are able to truncate the wave function (3) to the wave function describing only the evolution of the resonant states.…”

Section: The Model and Solutionsmentioning

confidence: 99%

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Finite-dimensional states and entanglement generation for a nonlinear coupler

Kowalewska-Kudłaszyk

Leoński

2006

Phys. Rev. A

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We discuss a system comprising two nonlinear (Kerr-like) oscillators coupled mutually by a nonlinear interaction. The system is excited by an external coherent field that is resonant to the frequency of one of the oscillators. We show that the coupler evolution can be closed within a finite set of n-photon states, analogously as in the nonlinear quantum scissors model. Moreover, for this type of evolution our system can be treated as a Bell-like states generator. Thanks to the nonlinear nature of both: oscillators and their internal coupling, these states can be generated even if the system exhibits its energy dissipating nature, contrary to systems with linear couplings.

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Section: The Model and Solutionsmentioning

confidence: 97%

Section: The Model and Solutionsmentioning

confidence: 99%

Finite-dimensional states and entanglement generation for a nonlinear coupler

Kowalewska-Kudłaszyk

Leoński

2006

Phys. Rev. A

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“…As a consequence, we can expect that in the evolution of the system many of the states corresponding to great number of photons will be involved. However, we can overcome this difficulty by applying the nonlinear quantum scissors method discussed in [24] (for the discussion concerning quantum states defined in finite-dimensional Hilbert spaces and the methods of their generation see the review papers [25,26] and the references cited therein). Namely, it is seen from the form ofĤ N L that this Hamiltonian produces degenerate levels of the energy equal to zero, corresponding to the following four states:…”

Section: The Model and Solutionsmentioning

confidence: 99%

“…We perform the calculations following the method discussed in [26], and first we construct the unitary evolution operatorÛ applying the full Hamiltonian shown in (1):…”

Section: The Model and Solutionsmentioning

confidence: 99%

Kerr nonlinear coupler and entanglement

Leoński¹,

Miranowicz²

2004

J. Opt. B: Quantum Semiclass. Opt.

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101

104

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We discuss a model comprising two coupled nonlinear oscillators (Kerr-like nonlinear coupler) with one of them pumped by an external coherent excitation. Applying the method of nonlinear quantum scissors we show that the quantum evolution of the coupler can be closed within a finite set of n-photon Fock states. Moreover, we show that the system is able to generate Bell-like states and, as a consequence, the coupler discussed behaves as a two-qubit system. We also analyze the effects of dissipation on entanglement of formation parametrized by concurrence.

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“…Alternatively, one can analyze states obtained by a direct truncation of operators rather then of their Fock expansion. Such an operator truncation scheme, proposed by Leoński et al [48,49,50], will be discussed in detail in the next chapter [51].…”

Section: Introductionmentioning

confidence: 99%