Quantum-interference effects on the superposition of N displaced number states

Marchiolli, Marcelo A.; Silva, Luciano F. da; Melo, Paulo S.; Dantas, Célia M.A.

doi:10.1016/s0378-4371(00)00529-x

Cited by 9 publications

(6 citation statements)

References 41 publications

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“…The statistical properties of these states exhibit several pure quantum effects which have no classical analogues, including the interference in the phase space [18], the revival/collapse phenomenon [19], and sub-Poissonian statistics [20]. The position representation of these states with overall phases is derived by Moller et al for the simple harmonic oscillator by employing geometric operations in phase space [17].…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

Choi

Kim

2013

Nanoscale Res Lett

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“…The combination of ( 7) and (11) results in a generalization of formulae found in [60] for the superpositions of coherent states (m = 0) and in [66] for m arbitrary (but in the special case of c k = 1 and…”

Section: Wigner Functions Of Superpositions Of Displaced Statesmentioning

confidence: 80%

“…The generation and amplification of displaced circular states were studied in [65]. Properties of the superpositions (4) with m 1 and c k = 1 were considered in [23,66]. The problem of decoherence of these states was considered in [23,24], but only for small values of parameters m and |α|.…”

Section: Introductionmentioning

confidence: 99%

Decoherence of multicomponent symmetrical superpositions of displaced quantum states

Dodonov¹,

Souza²

2007

J. Phys. A: Math. Theor.

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We study the decoherence of superpositions of displaced quantum states of the form N k=1 c k D(α k )|g (where |g is an arbitrary 'fiducial' state and D(α) is the usual displacement operator) within the framework of the standard master equation for a quantum damped or amplified harmonic oscillator interacting with a phase-insensitive (thermal) reservoir. We compare two simple measures of the degree of decoherence: the quantum purity and the height of the central interference peak of the Wigner function. We show that for N > 2 'mesoscopic' components of the superposition, the decoherence process cannot be characterized by a single decoherence time. Therefore, we distinguish the 'initial decoherence time' and 'final decoherence time' and study their dependence on the parameters α k and N. We obtain approximate formulae for an arbitrary state |g and explicit exact expressions in the special case of |g = |m , i.e., for (symmetrical) superpositions of displaced Fock states of occupation number m. We show that the superposition with a large number of components N and rich 'internal structure' (m ∼ |α| 2 ) can be more robust against decoherence than simple superpositions of two coherent states (with m = 0), even if the initial decoherence times coincide. Also, we show how initial pure quantum superpositions are transformed into highly mixed and totally classical superpositions in the case of a phase-insensitive amplifier.

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“…In order to calculate the time evolution of the Wigner function associated to the motional state |Ψ (2 ℓ+1 ) n (β) , firstly we substitute into the integrand of Eq. (16) the initial Wigner function [34] W n (p ′ , q ′ ; 0) = (−1) n π…”

Section: The Degradation Of the Quantum Interference Effects Via mentioning

confidence: 99%

“…In the present contribution, we propose a systematic scheme which permits us to engineer superpositions of displaced number states on a circle in phase space as target states for the CM motion of a trapped ion. These superpositions were studied by Marchiolli et al [34], where the authors have shown that (i) the interference effects among the state components present an analogy with diffraction patterns arising in an N slit Young-type experiment, and (ii) the interference and correlation effects are connected with the nondiagonal term of the quasiprobability distributions. In general, the superpositions of N displaced number states on a circle in phase space can be defined as follows:…”

Section: Introductionmentioning

confidence: 99%

Engineering superpositions of displaced number states of a trapped ion

Marchiolli¹,

José²

2004

Physica A: Statistical Mechanics and its Applications

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We present a protocol that permits the generation of a subtle with superposition with 2^(l+1) displaced number states on a circle in phase space as target state for the center-of-mass motion of a trapped ion. Through a sequence of 'l' cycles involving the application of laser pulses and no-fluorescence measurements, explicit expressions for the total duration of laser pulses employed in the sequence and probability of getting the ion in the upper electronic state during the 'l' cycles are obtained and analyzed in detail. Furthermore, assuming that the effective relaxation process of a trapped ion can be described in the framework of the standard master equation for the damped harmonic oscillator, we investigate the degradation of the quantum interference effects inherent to superpositions via Wigner function.Comment: 14 pages, 10 figure

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Quantum-interference effects on the superposition of N displaced number states

Cited by 9 publications

References 41 publications

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

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

Decoherence of multicomponent symmetrical superpositions of displaced quantum states

Engineering superpositions of displaced number states of a trapped ion

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