Quantum circuit analog of the dynamical Casimir effect

Fujii, Toshiyuki; Matsuo, Shigemasa; Hatakenaka, Noriyuki; Kurihara, Susumu; Zeilinger, Anton

doi:10.1103/physrevb.84.174521

Cited by 60 publications

(62 citation statements)

References 31 publications

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“…One may imagine other possible applications, for example, in molecular spectroscopy [46], theory of crystals, quantum optics [24], [66], and cavity quantum electrodynamics [12], [13], [22], [35], [67]. We believe in a dynamic character of the nature [28].…”

Section: Discussionmentioning

confidence: 99%

On a hidden symmetry of quantum harmonic oscillators

Lopez

Suslov

Vega-Guzmán

2013

Journal of Difference Equations and Applications

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Abstract. We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg Uncertainty Principle is presented.The purpose of this Letter is to elaborate on a "missing" class of solutions to the time-dependent Schrödinger equation for the simple harmonic oscillator in one dimension. We also provide an interesting computer-animated feature of these solutions -the phase space oscillations of the electron density and the corresponding probability distribution of the particle linear momentum. As a result, a dynamic visualization of the fundamental Heisenberg Uncertainty Principle [27] is given [45], [62]. Symmetry and Hidden SolutionsThe time-dependent Schrödinger equation for the simple harmonic oscillator,has the following six-parameter family of square integrable solutionswhere H n (x) are the Hermite polynomials [51] and On the other hand, the "dynamic harmonic oscillator states" (1.2)-(1.9) are eigenfunctions,of the time-dependent quadratic invariant,with the required operator identity [15], [54]:(1.12)Here, the time-dependent annihilation a (t) and creation a † (t) operators are explicitly given bywith p = i −1 ∂/∂x in terms of our solutions (1.4)-(1.9). These operators satisfy the canonical commutation relation, 14) and the oscillator-type spectrum (1.10) of the dynamic invariant E can be obtained in a standard way by using the Heisenberg-Weyl algebra of the rasing and lowering operators (a "second quantization" [1], [42], the Fock states): Here, ψ n (x, t) = e i(2n+1)γ(t) Ψ n (x, t) (1.16) is the relation to the wave functions (1.2) with ϕ n (t) = − (2n + 1) [68] and the references therein) have attracted substantial attention over the years because of their great importance in many advanced quantum problems. Examples are coherent and squeezed states, uncertainty relations, Berry's phase, quantization of mechanical systems and Hamiltonian cosmology. More applications include, but are not limited to charged particle traps and motion in uniform magnetic fields, molecular spectroscopy and polyatomic molecules in varying external fields, crystals through which an electron is passing and exciting the oscillator modes, and other mode interactions with external fields. Quadratic Hamiltonians have particular applications in quantum electrodynamics because the electromagnetic field can be represented as a set of generalized driven harmonic oscillators [13], [20].The maximal kinematical invariance group of the simple harmonic oscillator [50] provides the six-parameter family of solutions, namely (1.2) and (1.3)-(1.9), for an arbitrary choice of the initial data (of the corresp...

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Section: Discussionmentioning

confidence: 99%

On a hidden symmetry of quantum harmonic oscillators

Lopez

Suslov

Vega-Guzmán

2013

Journal of Difference Equations and Applications

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“…Quantum circuits LC with discrete charge have been intensely studied in the past decades due to their potential technological, nano-electronic, quantum computation and quantum information applications [11][12][13][14][15][16][17][18][19][20][21][22][23][24][29][30][31][32][33]. Therefore, the study of two coupled mesoscopic electric circuits LC with mutual inductance is very important both theoretically and experiment.…”

Section: Two Mesoscopic Electric Lc Circuits With Mutual-inductancementioning

confidence: 99%

An investigation of algebraic quantum dynamics for mesoscopic coupled electric circuits with mutual inductance

Pahlavani

Kolur

2016

Physica B: Condensed Matter

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“…The development of experimental techniques like quantum tomography [13] provided a possibility to measure the density matrices of quantum states and obtain, as the results of the experiments, numerical values of the matrix elements of the density matrices for qudits. Since the entropic and information characteristics of quantum states used in the experiments with superconducting circuits discussed, for example, in [14][15][16] are expressed in terms of the density matrix elements, it is desirable to have explicit formulas for the entropic inequalities containing the matrix elements. In this connection, we express some entropic inequalities known for multipartite systems in an explicit form to be applied for studying the states of the systems without subsystems.…”

Section: Introductionmentioning

confidence: 99%

Properties of Nonnegative Hermitian Matrices and New Entropic Inequalities for Noncomposite Quantum Systems

Man’ko

2015

Entropy

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We consider the probability distributions, spin (qudit)-state tomograms and density matrices of quantum states, and their information characteristics, such as Shannon and von Neumann entropies and q-entropies, from the viewpoints of both well-known purely mathematical features of nonnegative numbers and nonnegative matrices and their physical characteristics, such as entanglement and other quantum correlation phenomena. We review entropic inequalities such as the Araki-Lieb inequality and the subadditivity and strong subadditivity conditions known for bipartite and tripartite systems, and recently obtained for single qudit states. We present explicit matrix forms of the known and some new entropic inequalities associated with quantum states of composite and noncomposite systems. We discuss the tomographic probability distributions of qudit states and demonstrate the inequalities for tomographic entropies of the qudit states. In addition, we mention a possibility to use the discussed information properties of single qudit states in quantum technologies based on multilevel atoms and quantum circuits produced of Josephson junctions.

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Quantum circuit analog of the dynamical Casimir effect

Cited by 60 publications

References 31 publications

On a hidden symmetry of quantum harmonic oscillators

On a hidden symmetry of quantum harmonic oscillators

An investigation of algebraic quantum dynamics for mesoscopic coupled electric circuits with mutual inductance

Properties of Nonnegative Hermitian Matrices and New Entropic Inequalities for Noncomposite Quantum Systems

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