Displaced and squeezed number states

Nieto, Michael Martin

doi:10.1016/s0375-9601(97)00183-7

Cited by 119 publications

(119 citation statements)

References 32 publications

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“…Our result in Equation 44 is exact, and in this limit, we can easily confirm that some errors in Equation 45 in [30] are corrected (see Appendix Appendix 2).…”

Section: Methods and Resultssupporting

confidence: 74%

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Displacing, squeezing, and time evolution of quantum states for nanoelectronic circuits

Choi

Kim

2013

Nanoscale Res Lett

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The time behavior of DSN (displaced squeezed number state) for a two-dimensional electronic circuit composed of nanoscale elements is investigated using unitary transformation approach. The original Hamiltonian of the system is somewhat complicated. However, through unitary transformation, the Hamiltonian became very simple enough that we can easily treat it. By executing inverse transformation for the wave function obtained in the transformed system, we derived the exact wave function associated to the DSN in the original system. The time evolution of the DSN is described in detail, and its corresponding probability density is illustrated. We confirmed that the probability density oscillates with time like that of a classical state. There are two factors that drive the probability density to oscillate: One is the initial amplitude of complementary functions, and the other is the external power source. The oscillation associated with the initial amplitude gradually disappears with time due to the dissipation raised by resistances of the system. These analyses exactly coincide with those obtained from classical state. The characteristics of quantum fluctuations and uncertainty relations for charges and currents are also addressed.

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“…Our result in Equation 44 is exact, and in this limit, we can easily confirm that some errors in Equation 45 in [30] are corrected (see Appendix Appendix 2).…”

Section: Methods and Resultssupporting

confidence: 74%

“…Besides, among various functions that appeared in Equation 45 of [30],

{scriptF}_{3}

(Equation 23) and A (Equation 46) should be altered as …”

Section: Appendixmentioning

confidence: 99%

Displacing, squeezing, and time evolution of quantum states for nanoelectronic circuits

Choi

Kim

2013

Nanoscale Res Lett

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“…(12) in the transformed system, we easily obtain the corresponding wave functions in the number state and confirm that their initial values are given byThese are the same as those of the simple harmonic oscillator with the angular frequency . The action of a squeezing operator in the initial number state giveswhere Further action of and , in turn, yields [7, 33]where Let us consider superposition states composed of the two DSNSs in the transformed system, which iswhere is given by and is a normalization constant of which the formula will be derived later. The superposition states in the original system are obtained by acting in these states:A rigorous evaluation using Eq.…”

Section: Resultssupporting

confidence: 62%

Squeezing effects applied in nonclassical superposition states for quantum nanoelectronic circuits

Choi

2017

Nano Convergence

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Quantum characteristics of a driven series RLC nanoelectronic circuit whose capacitance varies with time are studied using an invariant operator method together with a unitary transformation approach. In particular, squeezing effects and nonclassical properties of a superposition state composed of two displaced squeezed number states of equal amplitude, but 180° out of phase, are investigated in detail. We applied our developments to a solvable specific case obtained from a suitable choice of time-dependent parameters. The pattern of mechanical oscillation of the amount of charges stored in the capacitor, which are initially displaced, has exhibited more or less distortion due to the influence of the time-varying parameters of the system. We have analyzed squeezing effects of the system from diverse different angles and such effects are illustrated for better understanding. It has been confirmed that the degree of squeezing is not constant, but varies with time depending on specific situations. We have found that quantum interference occurs whenever the two components of the superposition meet together during the time evolution of the probability density. This outcome signifies the appearance of nonclassical features of the system. Nonclassicality of dynamical systems can be a potential resource necessary for realizing quantum information technique. Indeed, such nonclassical features of superposition states are expected to play a key role in upcoming information science which has attracted renewed attention recently.

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“…A class of states (or wave packets in the configuration space) that are of special interest in the following are the so called displaced number states. Similar to those for a simple harmonic oscillator [21,22,23], they are defined as…”

Section: IImentioning

confidence: 99%

Geometric phases for wave packets in a uniform magnetic field

Lin

2002

Physics Letters A

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A wave packet of a charged particle always make cyclic circular motion in a uniform magnetic field, just like a classical particle. The nonadiabatic geometric phase for an arbitrary wave packet can be expressed in terms of the mean value of a number operator. For a large class of wave packets, the geometric phase is proportional to the magnetic flux encircled by the orbit of the wave packet. For more general wave packets, however, the geometric phase contains an extra term.

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Displaced and squeezed number states

Cited by 119 publications

References 32 publications

Displacing, squeezing, and time evolution of quantum states for nanoelectronic circuits

Displacing, squeezing, and time evolution of quantum states for nanoelectronic circuits

Squeezing effects applied in nonclassical superposition states for quantum nanoelectronic circuits

Geometric phases for wave packets in a uniform magnetic field

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