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

Quantum Electronics and Laser Science Conference

Quantum-state reconstruction of atoms in optical lattices

Sascha Wallentowitz, A. Zucchetti, W. Vogel, N. P. Bigelow

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

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.

Related papers

Quantum-state reconstruction of atoms in optical lattices

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

We propose a method to reconstruct the vibrational quantum state of atoms bound in arbitrary periodic potentials created by an optical lattice. The vibrational density matrix is determined from vibrational populations that are measured after translations of the optical-lattice potential. These translations are realized by phase shifts of the lattice laser fields. The feasibility of the reconstruction method is shown for a typical situation realized in recent experiments.

Physical Review A•Dec 9, 1999•4 citations

Quantum state control and characterization in an optical lattice

Stefan H. Myrskog

In this dissertation I present experimental work on the measurement and manipulation of the center-of-mass motion of laser-cooled atoms. The first experiment described demonstrates cooling of an atom cloud by 'delta-kick cooling'. A thermal cloud of atoms in a vacuum expands ballistically, generating correlations between position and momentum. An appropriate momentum kick, proportional to position, results in slowing down all the atoms in the cloud. Through this technique a cloud of atoms can be cooled by greater than a factor of 10, preserving phase-space density, but decreasing the number density of atoms. By using laser-cooled atoms, it is also possible to confine atoms in potentials created by the AC-Stark shift of the atomic energy levels. Using interfering lasers to create the Stark shift, atoms are confined in a sinusoidal potential called an optical lattice. After preparing atoms in the lowest-energy band of the lattice, a spatial displacement can create coherent superpositions of many states of the potential. A combination of time delays and secondary displacements allows the measurement of the Q (Husimi) and W (Wigner) quasi-probability distributions, each of which completely characterizes the motional state of the atoms. Alternatively, a shallow lattice that only support two long-lived states can be used. The two-state system may be characterized with far fewer measurements, and furthermore, can be used as a model system for a qubit, a quantum representation of a single bit of information, useful for quantum computation. We demonstrate reconstruction of the density matrix in the 2-state system. The two-state system has be further used to characterize the physical action of an operation. By preparing a complete set of input density matrices we perform quantum process tomography for the intrinsic decoherence of the lattice, and two operations that correspond to single qubit rotations.

•Jan 1, 2004•1 citation

Semi-classical and quantum Monte Carlo simulations in optical lattices

Stephen Peter Winklbauer

This thesis gives an account of work done on semi-classical and quantum Monte Carlo simulations in far-detuned optical lattices. Firstly, the basic principles of laser cooling of atoms are presented including a short introduction to optical lattices in the near and far-detuned regime. A detailed analysis is made of the band-structure of optical lattices, using the Bloch formalism, and of the bound-state population distribution appropriate for a thermal sample of trapped atoms. Secondly, a general overview is given of the quantum Monte Carlo method for simulating the dynamics of atom-light interactions. This is followed by a detailed study of the concept of Raman cooling, which is a useful tool to prepare atoms in the ground motional state of the lattice and an important first step to achieving quantum state control with ultra-cold atoms. A simplified model of Raman cooling is introduced and simulated using the quantum Monte Carlo wave-function approach. Then the implementation of simulations of resolved-sideband Raman cooling based on this model is discussed as is how the results were used to optimize the experimental work done by our group. The results of these simulations show for the first time that the quantum Zeno effect has a crucial impact on the efficiency of Raman cooling experiments. Also the experimental measurements of the temperature of Raman sideband cooled atoms for a range of parameters are compared with theoretical results and shows a good qualitative agreement. Thirdly, the results of semi-classical numerical simulations of parametric excitation in optical lattices are presented. It is shown that the modulation of the potential can result in selective parametric excitation of trapped atoms. The theoretical results show good qualitative agreement with experiment. The thesis is concluded with a description of possible avenues for future studies on quantum state control in optical lattices.

•Jan 1, 2004•0 citations

Quantum state preparation in an optical lattice

S. E. Hamann

This dissertation reports on quantum state preparation of cesium atoms in a two-dimensional optical lattice, by resolved-sideband Raman cooling. An optical lattice is a periodic potential produced by the light shift interaction between an atom and light field. Laser cooled atoms can become strongly localized about the bottom of potential wells in an optical lattice, where they occupy a discrete spectrum of bound vibrational energy levels. The distribution over vibrational levels of atoms in the lattice is characterized by the mean vibrational excitation, n . In an optical lattice, absorption and emission of photons from lattice beams causes n to increase in time. This source of heating is always present, but its rate can be greatly reduced in a lattice detuned far from the atomic resonance. Sideband cooling is an efficient means of transferring atoms from higher into lower-lying vibrational levels and, thus, it reduces n for the ensemble. If the sideband cooling rate is much greater than the heating rate, then n approaches zero and virtually all atoms are in the lowest vibrational level in their potential wells. Our sideband cooling scheme involves stimulated Raman transitions between bound states in the potential wells of a pair of magnetic sublevels, followed by optical pumping, for a net loss of one quantum of vibration per cooling cycle. The process accumulates 98% of atoms in the ground vibrational level of a potential well associated with a single Zeeman substate. Each atom in the lattice is then very close to a pure state. For two-dimensional lattice with sideband cooling we find nx≈ny≈0.008 &parl0;16&parr0; . Various issues related to state preparation and sideband cooling are also discussed in the context of a one dimensional lin ⊥ lin optical lattice. These include improvement of laser cooling in a near resonance lattice by application of weak magnetic fields, transfer of atoms from near into far off-resonance lattices, and heating rates in far off-resonance lattices.

•Jan 1, 1998•1 citation

Cooling atoms in a far-detuned optical lattice

David S. Weiss, S. Lukman Winoto, Mark T. Depue

A new method of studying and cooling trapped atoms is discussed, with particular attention to atoms in far detuned, 3D optical lattices. The technique, projection cooling, uses a combination of microwave and optical fields to cycle atoms between hyperfine sublevels. A single vibrational level will remain dark to both the light and the microwaves, so atoms will accumulate there. Cooling below the photon recoil limit is possible with this technique. As a diagnostic tool it promises to yield detailed information about atoms in the lattice, including vibrational spectra and the distribution of atoms among vibrational levels, even in the limit of relatively weak binding to lattice sites. Atoms cooled in this way and then allowed to adiabatically expand in their potentials could reach the Bose-Einstein condensation point in less than a second, or at least get close enough to reach it after only a modest amount of evaporative cooling in a larger volume trap. Atoms so cooled and trapped are also of interest for precision measurements.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 1, 1997•5 citations

Quantum correlations of ultracold atoms in optical lattices

Shuming Li

An optical lattice is the periodic potential that atoms experience via the ac-Stark shift when they are illuminated by counter-propagating laser beams that form a standing-wave pattern. Optical lattices have been widely used as a versatile platform in cooling, trapping, controlling atoms, and also for the study of a variety of problems in physics. The many-body states of ultracold atoms in optical lattices can be characterized by the quantum-correlations encoded in time-of-flight images. In this thesis, we mainly discuss the use of correlations function as a natural framework for characterizing quantum states in optical lattices.\nThe outline of the thesis is as follows. Chapter 1 gives a brief introduction to optical lattice potentials and ways for describing particles moving in a periodic potential. Chapter 2 explains the importance of correlations and discusses common methods to detect them in cold atom experiments.\nChapter 3 presents work done to study the many-body Schrödinger equation in a quasiperiodic potential and discusses its connection with the Kolmogorov-Arnold-Moser (KAM) problem of classical mechanics. We posed a possible visualization of such a connection in experimentally accessible many-body observables. These observables are useful probes for the three characteristic phases of the problem: the metallic, Anderson, and band-insulator phases. In addition, they exhibit fingerprints of nonlinear phenomena such as bifurcations and devil's staircases. Our numerical treatment is complemented with a perturbative analysis that provides insight on the underlying physics. The perturbative-theory approach is particularly useful in illuminating the distinction between the Anderson-insulator and the band-insulator phases in terms of paired sets of dimerized states.\nChapter 4 discusses several theoretical procedures developed to understand a recent experiment on macroscopic quantum self-trapping (ST) performed in a 2D optical lattice. Mean field and truncated-Wigner-approximation (TWA) calculations are performed trying to reproduce the experimental observations. The discrepancy between the theory and the experiment lead to the hypothesis of a new type of ST caused by strong correlations. We analyze toy models to support it.

•Jan 1, 2014•0 citations
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.
In this dissertation I present experimental work on the measurement and manipulation of the center-of-mass motion of laser-cooled atoms. The first experiment described demonstrates cooling of an atom cloud by 'delta-kick cooling'. A thermal cloud of atoms in a vacuum expands ballistically, generating correlations between position and momentum. An appropriate momentum kick, proportional to position, results in slowing down all the atoms in the cloud. Through this technique a cloud of atoms can be cooled by greater than a factor of 10, preserving phase-space density, but decreasing the number density of atoms. By using laser-cooled atoms, it is also possible to confine atoms in potentials created by the AC-Stark shift of the atomic energy levels. Using interfering lasers to create the Stark shift, atoms are confined in a sinusoidal potential called an optical lattice. After preparing atoms in the lowest-energy band of the lattice, a spatial displacement can create coherent superpositions of many states of the potential. A combination of time delays and secondary displacements allows the measurement of the Q (Husimi) and W (Wigner) quasi-probability distributions, each of which completely characterizes the motional state of the atoms. Alternatively, a shallow lattice that only support two long-lived states can be used. The two-state system may be characterized with far fewer measurements, and furthermore, can be used as a model system for a qubit, a quantum representation of a single bit of information, useful for quantum computation. We demonstrate reconstruction of the density matrix in the 2-state system. The two-state system has be further used to characterize the physical action of an operation. By preparing a complete set of input density matrices we perform quantum process tomography for the intrinsic decoherence of the lattice, and two operations that correspond to single qubit rotations.
This thesis gives an account of work done on semi-classical and quantum Monte Carlo simulations in far-detuned optical lattices. Firstly, the basic principles of laser cooling of atoms are presented including a short introduction to optical lattices in the near and far-detuned regime. A detailed analysis is made of the band-structure of optical lattices, using the Bloch formalism, and of the bound-state population distribution appropriate for a thermal sample of trapped atoms. Secondly, a general overview is given of the quantum Monte Carlo method for simulating the dynamics of atom-light interactions. This is followed by a detailed study of the concept of Raman cooling, which is a useful tool to prepare atoms in the ground motional state of the lattice and an important first step to achieving quantum state control with ultra-cold atoms. A simplified model of Raman cooling is introduced and simulated using the quantum Monte Carlo wave-function approach. Then the implementation of simulations of resolved-sideband Raman cooling based on this model is discussed as is how the results were used to optimize the experimental work done by our group. The results of these simulations show for the first time that the quantum Zeno effect has a crucial impact on the efficiency of Raman cooling experiments. Also the experimental measurements of the temperature of Raman sideband cooled atoms for a range of parameters are compared with theoretical results and shows a good qualitative agreement. Thirdly, the results of semi-classical numerical simulations of parametric excitation in optical lattices are presented. It is shown that the modulation of the potential can result in selective parametric excitation of trapped atoms. The theoretical results show good qualitative agreement with experiment. The thesis is concluded with a description of possible avenues for future studies on quantum state control in optical lattices.
This dissertation reports on quantum state preparation of cesium atoms in a two-dimensional optical lattice, by resolved-sideband Raman cooling. An optical lattice is a periodic potential produced by the light shift interaction between an atom and light field. Laser cooled atoms can become strongly localized about the bottom of potential wells in an optical lattice, where they occupy a discrete spectrum of bound vibrational energy levels. The distribution over vibrational levels of atoms in the lattice is characterized by the mean vibrational excitation, n . In an optical lattice, absorption and emission of photons from lattice beams causes n to increase in time. This source of heating is always present, but its rate can be greatly reduced in a lattice detuned far from the atomic resonance. Sideband cooling is an efficient means of transferring atoms from higher into lower-lying vibrational levels and, thus, it reduces n for the ensemble. If the sideband cooling rate is much greater than the heating rate, then n approaches zero and virtually all atoms are in the lowest vibrational level in their potential wells. Our sideband cooling scheme involves stimulated Raman transitions between bound states in the potential wells of a pair of magnetic sublevels, followed by optical pumping, for a net loss of one quantum of vibration per cooling cycle. The process accumulates 98% of atoms in the ground vibrational level of a potential well associated with a single Zeeman substate. Each atom in the lattice is then very close to a pure state. For two-dimensional lattice with sideband cooling we find nx≈ny≈0.008 &parl0;16&parr0; . Various issues related to state preparation and sideband cooling are also discussed in the context of a one dimensional lin ⊥ lin optical lattice. These include improvement of laser cooling in a near resonance lattice by application of weak magnetic fields, transfer of atoms from near into far off-resonance lattices, and heating rates in far off-resonance lattices.
A new method of studying and cooling trapped atoms is discussed, with particular attention to atoms in far detuned, 3D optical lattices. The technique, projection cooling, uses a combination of microwave and optical fields to cycle atoms between hyperfine sublevels. A single vibrational level will remain dark to both the light and the microwaves, so atoms will accumulate there. Cooling below the photon recoil limit is possible with this technique. As a diagnostic tool it promises to yield detailed information about atoms in the lattice, including vibrational spectra and the distribution of atoms among vibrational levels, even in the limit of relatively weak binding to lattice sites. Atoms cooled in this way and then allowed to adiabatically expand in their potentials could reach the Bose-Einstein condensation point in less than a second, or at least get close enough to reach it after only a modest amount of evaporative cooling in a larger volume trap. Atoms so cooled and trapped are also of interest for precision measurements.
An optical lattice is the periodic potential that atoms experience via the ac-Stark shift when they are illuminated by counter-propagating laser beams that form a standing-wave pattern. Optical lattices have been widely used as a versatile platform in cooling, trapping, controlling atoms, and also for the study of a variety of problems in physics. The many-body states of ultracold atoms in optical lattices can be characterized by the quantum-correlations encoded in time-of-flight images. In this thesis, we mainly discuss the use of correlations function as a natural framework for characterizing quantum states in optical lattices.\nThe outline of the thesis is as follows. Chapter 1 gives a brief introduction to optical lattice potentials and ways for describing particles moving in a periodic potential. Chapter 2 explains the importance of correlations and discusses common methods to detect them in cold atom experiments.\nChapter 3 presents work done to study the many-body Schrödinger equation in a quasiperiodic potential and discusses its connection with the Kolmogorov-Arnold-Moser (KAM) problem of classical mechanics. We posed a possible visualization of such a connection in experimentally accessible many-body observables. These observables are useful probes for the three characteristic phases of the problem: the metallic, Anderson, and band-insulator phases. In addition, they exhibit fingerprints of nonlinear phenomena such as bifurcations and devil's staircases. Our numerical treatment is complemented with a perturbative analysis that provides insight on the underlying physics. The perturbative-theory approach is particularly useful in illuminating the distinction between the Anderson-insulator and the band-insulator phases in terms of paired sets of dimerized states.\nChapter 4 discusses several theoretical procedures developed to understand a recent experiment on macroscopic quantum self-trapping (ST) performed in a 2D optical lattice. Mean field and truncated-Wigner-approximation (TWA) calculations are performed trying to reproduce the experimental observations. The discrepancy between the theory and the experiment lead to the hypothesis of a new type of ST caused by strong correlations. We analyze toy models to support it.