Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0506140 · Journal of Optics B Quantum and Semiclassical Optics

Phase space tomography of classical and nonclassical vibrational states of atoms in an optical lattice

J. F. Kanem, Samansa Maneshi, Stefan H. Myrskog, Aephraim M. Steinberg

Published Nov 22, 2005• 14 citations
arXivHTMLPDF

Abstract

Atoms trapped in an optical lattice have long been a system of interest in the atomic, molecular and optical community, and in recent years much study has been devoted to both short- and long-range coherence in this system, as well as to its possible applications to quantum information processing. Here we demonstrate for the first time a complete determination of the quantum phase space distributions for an ensemble of 85 Rb atoms in such a lattice, including a negative Wigner function for atoms in an inverted state.

DOI
10.1088/1464-4266/7/12/037

Related papers

Quantum process tomography on vibrational states of atoms in an optical lattice

Stefan H. Myrskog, J. K. Fox, Morgan W. Mitchell +1 more

Quantum process tomography is used to fully characterize the evolution of the quantum vibrational state of atoms. Rubidium atoms are trapped in a shallow optical lattice supporting only two vibrational states, which we characterize by reconstructing the $2\ifmmode\times\else\texttimes\fi{}2$ density matrix. Repeating this reconstruction for a complete set of inputs allows us to completely characterize both the system's intrinsic decoherence and resonant coupling.

arXiv:quant-ph/0312210•Physical Review A•Jul 25, 2005•59 citations

Quantum-state reconstruction of atoms in optical lattices

Sascha Wallentowitz, A. Zucchetti, W. Vogel +1 more

Summary form only given. The preparation of the quantum state of physical systems and its diagnostics by quantum-state reconstruction has been a subject of large progress in recent years. Various experiments have successfully demonstrated the feasibility of reconstructing the quantum state of optical fields, molecular vibrations, trapped ions, and matter waves. The impressive success in laser cooling of neutral atoms opens new possibilities for preparing quantum states of ensembles of atoms in optical lattices and also quantum computing. In this context, the diagnostics of the quantum state, would provide a very useful tool for studying the accuracy of prepared quantum states or exploring decoherence mechanisms. However, to our knowledge, a reconstruction method for optical lattices that accounts for typical features of optical lattice potentials such as anharmonicity and band structure, is not yet available. We propose such a method, that we think is relatively simple to implement, since only phase shifts of the lattice laser beams and measurements of the band populations in the lattice potential are needed. These techniques are feasible by use of electro/acousto-optical modulators and by measuring the momentum distribution of the atoms after adiabatically turning off the lattice lasers.

Quantum Electronics and Laser Science Conference•Jan 1, 2000•0 citations

Phase-space distributions of Bose–Einstein condensates in an optical lattice: optimal shaping and reconstruction

Nathan Dupont, Floriane Arrouas, Lucas Gabardos +5 more

Abstract We apply quantum optimal control to shape the phase-space distribution of Bose–Einstein condensates in a one-dimensional optical lattice. By a time-dependent modulation of the lattice position, determined from optimal control theory, we prepare, in the phase space of each lattice site, translated and squeezed Gaussian states, and superpositions of Gaussian states. Complete reconstruction of these non-trivial states is performed through a maximum likelihood state tomography. As a practical application of our method to quantum simulations, we initialize the atomic wavefunction in an optimal Floquet-state superposition to enhance dynamical tunneling signals.

arXiv:2210.11112•New Journal of Physics•Jan 1, 2023•17 citations

Complete experimental characterization of the quantum state of a light mode via the Wigner function and the density matrix: application to quantum phase distributions of vacuum and squeezed-vacuum states

D. T. Smithey, M. Beck, J. Cooper +2 more

We have used the recently demonstrated method of optical homodyne tomography (OHT) to measure the Wigner quasiprobability distribution (Wigner function) and the density matrix for both a squeezed-vacuum and a vacuum state of a single spatial-temporal mode of the electromagnetic field. This method consists of measuring a set of probability distributions for many different Hilbert-space representations of the field-quadrature amplitude, using balanced homodyne detection, and then using tomography to obtain the Wigner function. Once the Wigner function is obtained, one can acquire the density matrix, including its complex phase. In the case of a pure state, this technique yields an experimentally determined complex wavefunction, as demonstrated here for the vacuum. The density matrix represents a complete quantum mechanical characterization of the state. From the measured density matrix we have obtained the Pegg–Barnett optical phase distribution, and from the Wigner function, the Wigner optical phase distribution.

Physica Scripta•Jan 1, 1993•156 citations

Experimental determination of quantum phase distributions by using optical homodyne tomography

M. Beck, D. T. Smithey, M. G. Raymer

Using the new technique of optical homodyne tomography, we have measured the Wigner function and density matrix of an electromagnetic field mode. These quantities can be used to determine the distribution of any theoretically defined optical phase, as long as the phase reference is that of a strong coherent-state field.

Quantum Electronics and Laser Science Conference•May 2, 1993•0 citations

Engineering And Tomography Of Quantum States Of Motion Of A Trapped Atom

Dietrich G. Leibfried, D. M. Meekhof, Christopher R. Monroe +3 more

Summary form only given, as follows. The ability to create and completely characterize a variety of fundamental quantum states has long been sought after in the laboratory since it brings to the forefront issues involving the relationship between quantum and classical physics. The interaction of a trapped atom with classical laser light constitutes a simple and well-isolated quantum system that makes experiments along these lines possible. The motion of an ion trapped in a rf-trap can be described as a quantum harmonic oscillator. If the ion is driven by a classical light field, several interactions similar to and beyond the simple Jaynes-Cummings coupling can be realized. These couplings allow for precisely controlled engineering and measurement of quantum states. We create states having both classical and nonclassical character including thermal, number, coherent, squeezed, and Schrodinger cat states. The motional quantum state is fully reconstructed with use of two novel schemes that determine the density matrix in the number state basis and the Wigner function. Our techniques allow well-controlled experiments on decoherence and related phenomena on the quantum-classical borderline.

Quantum Electronics and Laser Science Conference•Jan 1, 1997•0 citations
Atoms trapped in an optical lattice have long been a system of interest in the atomic, molecular and optical community, and in recent years much study has been devoted to both short- and long-range coherence in this system, as well as to its possible applications to quantum information processing. Here we demonstrate for the first time a complete determination of the quantum phase space distributions for an ensemble of 85 Rb atoms in such a lattice, including a negative Wigner function for atoms in an inverted state.
Summary form only given. The preparation of the quantum state of physical systems and its diagnostics by quantum-state reconstruction has been a subject of large progress in recent years. Various experiments have successfully demonstrated the feasibility of reconstructing the quantum state of optical fields, molecular vibrations, trapped ions, and matter waves. The impressive success in laser cooling of neutral atoms opens new possibilities for preparing quantum states of ensembles of atoms in optical lattices and also quantum computing. In this context, the diagnostics of the quantum state, would provide a very useful tool for studying the accuracy of prepared quantum states or exploring decoherence mechanisms. However, to our knowledge, a reconstruction method for optical lattices that accounts for typical features of optical lattice potentials such as anharmonicity and band structure, is not yet available. We propose such a method, that we think is relatively simple to implement, since only phase shifts of the lattice laser beams and measurements of the band populations in the lattice potential are needed. These techniques are feasible by use of electro/acousto-optical modulators and by measuring the momentum distribution of the atoms after adiabatically turning off the lattice lasers.
Abstract We apply quantum optimal control to shape the phase-space distribution of Bose–Einstein condensates in a one-dimensional optical lattice. By a time-dependent modulation of the lattice position, determined from optimal control theory, we prepare, in the phase space of each lattice site, translated and squeezed Gaussian states, and superpositions of Gaussian states. Complete reconstruction of these non-trivial states is performed through a maximum likelihood state tomography. As a practical application of our method to quantum simulations, we initialize the atomic wavefunction in an optimal Floquet-state superposition to enhance dynamical tunneling signals.
We have used the recently demonstrated method of optical homodyne tomography (OHT) to measure the Wigner quasiprobability distribution (Wigner function) and the density matrix for both a squeezed-vacuum and a vacuum state of a single spatial-temporal mode of the electromagnetic field. This method consists of measuring a set of probability distributions for many different Hilbert-space representations of the field-quadrature amplitude, using balanced homodyne detection, and then using tomography to obtain the Wigner function. Once the Wigner function is obtained, one can acquire the density matrix, including its complex phase. In the case of a pure state, this technique yields an experimentally determined complex wavefunction, as demonstrated here for the vacuum. The density matrix represents a complete quantum mechanical characterization of the state. From the measured density matrix we have obtained the Pegg–Barnett optical phase distribution, and from the Wigner function, the Wigner optical phase distribution.
Summary form only given, as follows. The ability to create and completely characterize a variety of fundamental quantum states has long been sought after in the laboratory since it brings to the forefront issues involving the relationship between quantum and classical physics. The interaction of a trapped atom with classical laser light constitutes a simple and well-isolated quantum system that makes experiments along these lines possible. The motion of an ion trapped in a rf-trap can be described as a quantum harmonic oscillator. If the ion is driven by a classical light field, several interactions similar to and beyond the simple Jaynes-Cummings coupling can be realized. These couplings allow for precisely controlled engineering and measurement of quantum states. We create states having both classical and nonclassical character including thermal, number, coherent, squeezed, and Schrodinger cat states. The motional quantum state is fully reconstructed with use of two novel schemes that determine the density matrix in the number state basis and the Wigner function. Our techniques allow well-controlled experiments on decoherence and related phenomena on the quantum-classical borderline.