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:1309.1672 · Physical Review Letters

Condensate Phase Microscopy

Arkadiusz Kosior, Krzysztof Sacha

Published Jan 29, 2014• 10 citations
arXivHTMLPDF

Abstract

We show that the phase of a Bose-Einstein condensate wave function of ultracold atoms in an optical lattice potential in two dimensions can be detected. The time-of-flight images, obtained in a free expansion of initially trapped atoms, are related to the initial distribution of atomic momenta but the information on the phase is lost. However, the initial atomic cloud is bounded and this information, in addition to the time-of-flight images, is sufficient in order to employ the phase retrieval algorithms. We analyze the phase retrieval methods for model wave functions in a case of a Bose-Einstein condensate in a triangular optical lattice in the presence of artificial gauge fields.

DOI
10.1103/physrevlett.112.045302

Related papers

Measuring the phase of a Bose-Einstein condensate

Andrew V. Martin, Leslie J. Allen

The phase of the mean-field wave function of a Bose-Einstein condensate can be recovered from a time series of images. We adapt an iterative retrieval method that has been successful in linear electron and optical imaging systems to solve the nonlinear Gross-Pitaevskii equation. We address a number of issues related to the successful application of this method to the nonlinear system, including the retrieval of wave functions with nonzero net topological charge (i.e., containing vortices) and the effects of repulsive and attractive interactions in the condensate on the convergence properties of the method. Recovering the phase from the continuity-of-density equation is also investigated. An understanding of these issues is of importance for the practical implementation of phase retrieval to Bose-Einstein condensates.

Physical Review A•Nov 8, 2007•5 citations

Expansion of a Coherent Array of Bose-Einstein Condensates

P. Pedri, Лев П. Питаевский, S. Stringari +6 more

We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wave function. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population, as well as the radial size of the expanding cloud are in good agreement with the predictions of theory. The 2D nature of the trapped condensates and the conditions required to observe the effects of coherence are also discussed.

arXiv:cond-mat/0108004•Physical Review Letters•Nov 12, 2001•193 citations

Signal of Bose-Einstein condensation in an optical lattice at finite temperature

Wei Yi, Guin-Dar Lin, L.-M. Duan

We discuss the experimental signal for the Bose-Einstein condensation of cold atoms in an optical lattice at finite temperature. Instead of using the visibility of the interference pattern via time-of-flight imaging, we show that the momentum-space density profile in the first Brillouin zone, in particular its bimodal distribution, provides an unambiguous signal for the Bose-Einstein condensation. We confirm this point with detailed calculations of the change in the atomic momentum distribution across the condensation phase transition, taking into account both the global trapping potential and the atomic interaction effects.

arXiv:0705.4352•Physical Review A•Sep 17, 2007•17 citations

Dynamics and phase evolution of Bose-Einstein condensates in one-dimensional optical lattices

O. Morsch, Matteo Cristiani, Jörg Helge Müller +2 more

We report experimental results on the dynamics and phase evolution of Bose-Einstein condensates in 1D optical lattices. The dynamical behaviour is studied by adiabatically loading the condensate into the lattice and subsequently switching off the magnetic trap. In this case, the condensate is free to expand inside the periodic structure of the optical lattice. The phase evolution of the condensate, on the other hand, can be studied by non-adiabatically switching on the periodic potential. We observe decays and revivals of the interference pattern after a time-of-flight.

arXiv:cond-mat/0209024•Sep 2, 2002•3 citations

Bose–Einstein Condensates in a One-Dimensional Optical Lattice: from Superfluidity to Number-Squeezed States

Xiaorui Wang, Lu Yang, Tan Xin-Zhou +2 more

We study the phase coherence property of Bose−Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza–Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.

Chinese Physics Letters•Aug 1, 2009•1 citation

Characteristics of Bose-Einstein condensation in an optical lattice

Guin-Dar Lin, Wei Zhang, L.-M. Duan

We discuss several possible experimental signatures of the Bose-Einstein condensation (BEC) transition for an ultracold Bose gas in an inhomogeneous optical lattice. Based on the commonly used time-of-flight imaging technique, we show that the momentum-space density profile in the first Brillouin zone, supplemented by the visibility of interference patterns, provides valuable information about the system. In particular, by crossing the BEC transition temperature, the appearance of a clear bimodal structure sets a qualitative and universal signature of this phase transition. Furthermore, the momentum distribution can also be applied to extract the condensate fraction, which may serve as a promising thermometer in such a system.

arXiv:0802.0700•Physical Review A•Apr 23, 2008•27 citations
We show that the phase of a Bose-Einstein condensate wave function of ultracold atoms in an optical lattice potential in two dimensions can be detected. The time-of-flight images, obtained in a free expansion of initially trapped atoms, are related to the initial distribution of atomic momenta but the information on the phase is lost. However, the initial atomic cloud is bounded and this information, in addition to the time-of-flight images, is sufficient in order to employ the phase retrieval algorithms. We analyze the phase retrieval methods for model wave functions in a case of a Bose-Einstein condensate in a triangular optical lattice in the presence of artificial gauge fields.
The phase of the mean-field wave function of a Bose-Einstein condensate can be recovered from a time series of images. We adapt an iterative retrieval method that has been successful in linear electron and optical imaging systems to solve the nonlinear Gross-Pitaevskii equation. We address a number of issues related to the successful application of this method to the nonlinear system, including the retrieval of wave functions with nonzero net topological charge (i.e., containing vortices) and the effects of repulsive and attractive interactions in the condensate on the convergence properties of the method. Recovering the phase from the continuity-of-density equation is also investigated. An understanding of these issues is of importance for the practical implementation of phase retrieval to Bose-Einstein condensates.
We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wave function. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population, as well as the radial size of the expanding cloud are in good agreement with the predictions of theory. The 2D nature of the trapped condensates and the conditions required to observe the effects of coherence are also discussed.
We discuss the experimental signal for the Bose-Einstein condensation of cold atoms in an optical lattice at finite temperature. Instead of using the visibility of the interference pattern via time-of-flight imaging, we show that the momentum-space density profile in the first Brillouin zone, in particular its bimodal distribution, provides an unambiguous signal for the Bose-Einstein condensation. We confirm this point with detailed calculations of the change in the atomic momentum distribution across the condensation phase transition, taking into account both the global trapping potential and the atomic interaction effects.
We report experimental results on the dynamics and phase evolution of Bose-Einstein condensates in 1D optical lattices. The dynamical behaviour is studied by adiabatically loading the condensate into the lattice and subsequently switching off the magnetic trap. In this case, the condensate is free to expand inside the periodic structure of the optical lattice. The phase evolution of the condensate, on the other hand, can be studied by non-adiabatically switching on the periodic potential. We observe decays and revivals of the interference pattern after a time-of-flight.
We study the phase coherence property of Bose−Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza–Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.
We discuss several possible experimental signatures of the Bose-Einstein condensation (BEC) transition for an ultracold Bose gas in an inhomogeneous optical lattice. Based on the commonly used time-of-flight imaging technique, we show that the momentum-space density profile in the first Brillouin zone, supplemented by the visibility of interference patterns, provides valuable information about the system. In particular, by crossing the BEC transition temperature, the appearance of a clear bimodal structure sets a qualitative and universal signature of this phase transition. Furthermore, the momentum distribution can also be applied to extract the condensate fraction, which may serve as a promising thermometer in such a system.