Squeezing and minimum uncertainty states in the supersymmetric harmonic oscillator

Orszag, Miguel; Salamó, S.

doi:10.1088/0305-4470/21/22/004

Cited by 27 publications

(16 citation statements)

References 9 publications

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“…Note that the exact factorization for the zero detuning ⑀ = 0 and strong coupling = 1 encountered in the literature 13 does not contradict our result. Note that the exact factorization for the zero detuning ⑀ = 0 and strong coupling = 1 encountered in the literature 13 does not contradict our result.…”

Section: ͑515͒supporting

confidence: 77%

Ladder operators and coherent states for the Jaynes-Cummings model in the rotating-wave approximation

Hussin

Nieto

2005

Journal of Mathematical Physics

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Transition of beam dynamics in waveguide arrays with commensurate Stark ladders Appl. Phys. Lett. 100, 041115 (2012) Two-bit quantum random number generator based on photon-number-resolving detection Rev. Sci. Instrum. 82, 073109 (2011) Decoherence and surface hopping: When can averaging over initial conditions help capture the effects of wave packet separation? J. Chem. Phys. 134, 244114 (2011) Photon counting statistics of single molecule in solid matrix JCP: BioChem.Using algebraic techniques, we realize a systematic search of different types of ladder operators for the Jaynes-Cummings model in the rotating-wave approximation. The link between our results and previous studies on the diagonalization of the associated Hamiltonian is established. Using some of the ladder operators obtained before, examples are given on the possibility of constructing a variety of interesting coherent states for this Hamiltonian.

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Section: ͑515͒supporting

confidence: 77%

Ladder operators and coherent states for the Jaynes-Cummings model in the rotating-wave approximation

Hussin

Nieto

2005

Journal of Mathematical Physics

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“…We have demonstrate that the SAES associated to the H-W Lie superalgebra contain the sets of standard coherent and supercoherent states associated to the usual and supersymmetric harmonic oscillator systems, respectively [2,3,14,21]. Also, these SAES contain both the standard squeezed and supersqueezed states [18,19] and the supersqueezed states associated to the spin- to the SAES the interpretation of an operator associated to a physical system, we have constructed some classes of superHermitian and η-pseudo-superHermitian Hamiltonians [12,17], isospectral to the standard harmonic oscillator hamiltonian. We have found their physical eigenstates and their associated supercoherent states.…”

Section: Discussionmentioning

confidence: 91%

“…We expect to recover the usual algebra eigenstates [2,3,19] but also supercoherent and supersqueezed states based on a group theoretical approach [16,18].…”

Section: Definition 11mentioning

confidence: 99%

sh(2/2) Superalgebra Eigenstates and Generalized Supercoherent and Supersqueezed States

Alvarez-Moraga

Hussin

2004

International Journal of Theoretical Physics

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The superalgebra eigenstates (SAES) concept is introduced and then applied to find the SAES associated to the sh(2/2) superalgebra, also known as Heisenberg-Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the sh(2/2) SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2) + ⊃ sh(2/2) superalgebra, where osp(2/2) denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg-Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the superHermitian and η-pseudo-superHermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.

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“…The SSs were also derived with a displacement operator using a supergroup [8]. It was shown that the three equivalent approaches are not equivalent [7]. But it was argued that the nonequivalency arises from the definition of the annihilation operator [10].…”

Section: Introductionmentioning

confidence: 99%

Quaternionic vector coherent states and the supersymmetric harmonic oscillator

2006

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The quaternionic vector coherent states are realized as coherent states of the supersymmetric harmonic oscillator with broken symmetry in analogy with the standard canonical coherent states of the ordinary harmonic oscillator. We study the nonclassical properties of the oscillator, such as the photon number distribution and signal-to-quantum-noise ratio in terms of these states and discuss the squeezing properties and the temporal stability of the coherent states. We obtain the orthogonal polynomials associated with the quaternionic vector coherent states.

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Squeezing and minimum uncertainty states in the supersymmetric harmonic oscillator

Cited by 27 publications

References 9 publications

Ladder operators and coherent states for the Jaynes-Cummings model in the rotating-wave approximation

Ladder operators and coherent states for the Jaynes-Cummings model in the rotating-wave approximation

sh(2/2) Superalgebra Eigenstates and Generalized Supercoherent and Supersqueezed States

Quaternionic vector coherent states and the supersymmetric harmonic oscillator

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