Simulation of tunneling in the quantum tomography approach

Lozovik, Yu. E.; Sharapov, V. A.; Arkhipov, A. S.

doi:10.1103/physreva.69.022116

Cited by 15 publications

(15 citation statements)

References 40 publications

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“…Here, we consider N d = 1 for simplicity; generalizing to the case of more variables and to the center-of-mass tomography is straightforward. Evolution equation (19) for the tomogram can be rewritten in the form [10], [23] w − µ m…”

Section: The Computer Simulation Methods In the Quantum Tomography Appmentioning

confidence: 99%

“…In this section, we describe the computer simulation method developed for the symplectic tomography [10]. Here, we consider N d = 1 for simplicity; generalizing to the case of more variables and to the center-of-mass tomography is straightforward.…”

Section: The Computer Simulation Methods In the Quantum Tomography Appmentioning

confidence: 99%

“…It appears that the tomogram is a measurable quantity that can be used in experiments on nonclassical and coherent states of light or atoms in matter optics [7]- [9]. On the other hand, the nonnegativity of the state-description function in the tomographic representation attracts those who simulate quantum systems [10] because many problems in the field arise when the values used to describe the state can be negative or even complex (e.g., the sign problem in Fermi system simulations). Tomography is also applicable in quantum computations and entanglement (see, e.g., [11]), as well as in the theory of information and signal analysis [8].…”

Section: Introductionmentioning

confidence: 99%

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Center-of-mass tomography and probability representation of quantum states for tunneling

et al. 2005

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We develop a representation of quantum states in which the states are described by fair probability distribution functions instead of wave functions and density operators. We present a one-random-variable tomography map of density operators onto the probability distributions, the random variable being analogous to the center-of-mass coordinate considered in reference frames rotated and scaled in the phase space. We derive the evolution equation for the quantum state probability distribution and analyze the properties of the map. To illustrate the advantages of the new tomography representations, we describe a new method for simulating nonstationary quantum processes based on the tomography representation. The problem of the nonstationary tunneling of a wave packet of a composite particle, an exciton, is considered in detail.

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Section: The Computer Simulation Methods In the Quantum Tomography Appmentioning

confidence: 99%

Section: The Computer Simulation Methods In the Quantum Tomography Appmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Center-of-mass tomography and probability representation of quantum states for tunneling

et al. 2005

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“…The tomographic map can be used not only for the description of the state in terms of a probability distributions, but also to describe its evolution (quantum transitions) by means of the standard real positive transition probabilities (alternative to the complex transition probability amplitude), i.e., in tunnelling dynamics [23]. Many-body 1D gases.…”

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confidence: 99%

Symplectic tomography of ultracold gases in tight waveguides

2008

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The phase space is the natural ground to smoothly extrapolate between local and non-local correlation functions. With this objective, we introduce the symplectic tomography of many-body quantum gases in tight-waveguides, and concentrate on the reduced single-particle symplectic tomogram (RSPST) whose marginals are the density profile and momentum distribution. We present an operational approach to measure the RSPST from the time evolution of the density profile after shutting off the interactions in a variety of relevant situations: free expansion, fall under gravity, and oscillations in a harmonic trap. From the RSPST, the one-body density matrix of the trapped state can be reconstructed. At low densities, ultracold bosonic gases exhibits universality. The interatomic interactions are then well described by the Fermi-Huang pseudo-potential, parametrized by a the 3D s-wave scattering length a s . If such gases are further confined in tight-waveguides, whenever the transverse excitation quantumhω ⊥ is larger than the longitudinal zero point and thermal energies, the system effectively becomes one-dimensional [1]. The interparticle pseudo-potential is then a simple delta function, so the system is well approximated by the LiebLiniger model [2]. Moreover, the strength of the interaction as a function of a s exhibits a confinement-induced 1D Feshbach resonance (CIR) [1,3], allowing to tune the 1D coupling constant g 1D from −∞ to +∞ and to reach both weak and strongly interacting regimes [4]. As a consequence, paradigmatic examples of the Bose-Fermi duality have been explored such as the Tonks-Girardeau gas [5], in which the strongly repulsive interactions between bosons leads to an effective Pauli exclusion principle [6]. In this regime, the system undergoes fermionization, all local correlation functions being identical to those of the spin-polarized ideal Fermi gas. Actually, the Fermi-Bose duality comes into play even with finite interactions [7]. However, quantum statistics invariably imposes an underlying signature manifested when looking at non-local correlations such as the momentum distribution or the one-body density matrix [8,9,10,11,12,13]. A natural ground to smoothly extrapolate between local and non-local correlations is the phase space. In this paper, we shall undertake the description of ultracold gases in tight-waveguides by means of the quantum tomographic technique [14]. We show that after shutting off the interactions in the system, the time evolution of the density profile governed by a quadratic Hamiltonian is tanta-

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“…In another line of studies, simulation of quantum systems have been performed using tomography. For example, tomograms were used for simulation of tunneling [25][26][27] and multimode quantum states [28]. Attempts have also been made to understand the tomogram via path integrals [29,30].…”

Section: Introductionmentioning

confidence: 99%

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

2016

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Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.

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Simulation of tunneling in the quantum tomography approach

Cited by 15 publications

References 40 publications

Center-of-mass tomography and probability representation of quantum states for tunneling

Center-of-mass tomography and probability representation of quantum states for tunneling

Symplectic tomography of ultracold gases in tight waveguides

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

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