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

Physical Review A

Measurement theory and interference of spinor Bose-Einstein condensates

Sahel Ashhab, A. J. Leggett

Published Jan 17, 2002• 21 citations
Publisher

Abstract

We study two aspects of measurement theory in spinor Bose-Einstein condensates of $F=1$ atoms: the probability of obtaining a certain outcome of the measurement and the evolution of the state of the condensate due to the measurement. We also study the interference patterns arising from the spatial overlap of two spinor condensates. We show that neither a measurement on a small number of escaping atoms nor an interference experiment can distinguish between an antiferromagnetic coherent state condensate, i.e., a condensate in which all the atoms have ${S}_{z}=0$ along an a priori unknown direction, and a spin-singlet condensate, i.e., a condensate with ${S}_{\mathrm{total}}=0.$ We also show that a singlet-state condensate evolves into a coherent state as a result of the measurement.

DOI
10.1103/physreva.65.023604

Related papers

Measurement theory for spinor condensates

Juha Javanainen

Abstract. We study the experimental signatures of several states of a Bose-Einstein condensate of spin-1 atoms by quantum trajectory simulations of Stern-Gerlach experiments. The measurement process itself creates an apparent random alignment for the spins, so that it is difficult to distinguish between a condensate that initially has an alignment in an unknown direction and one with no alignment at all. Nonetheless, in repeated experiments with identically prepared condensates, it is possible to discriminate between certain ground states of the condensate proposed in the literature. PACS numbers: 03.75.Fi,03.65.BzMeasurement theory for spinor condensates 2 1.

•Jan 1, 2000•3 citations

Topics in the Theory of Bose -Einstein Condensates With a Spin Degree of Freedom

Sahel Ashhab

We study several problems in Bose-Einstein condensates with internal degrees of freedom, and we find that this kind of condensates, which are usually referred to as spinor condensates, exhibit several phenomena that are qualitatively different from scalar (i.e. spinless) condensates. We analyze the ground state of a condensate with the constraint of maintaining a constant value of the total spin, and we find a number of different structures depending on the value of the total spin and the applied external magnetic field. We also study a certain type of measurement on spinor condensates in an attempt to distinguish between the so-called coherent and singlet states. We find that this kind of measurement cannot distinguish between the two states in question. We then consider a different experiment based on the interference between spinor condensate. It turns out that interference experiments cannot be used to distinguish between coherent and singlet states either. One of the interesting results regarding interference between two spinor condensates is that both the offset and visibility of the interference fringes vary from shot to shot, even if the initial conditions are identical in all the runs of the experiment. We then turn to the problem of condensing a gas of effectively spin 1/2 atoms. We argue that if spin relaxation mechanisms are slow enough, the condensate displays the phenomenon of fragmentation. The main difference of the fragmented state that we study and other fragmented states discussed in the literature is that this one is not caused by interatomic interactions, but rather by the constraint on the total spin of the system. We investigate the consequences of performing the experiment in a toroidal trap, and we find that, under certain conditions, the system spontaneously builds up a macroscopic value of orbital angular momentum. We finally discuss several problems related to the external Josephson effect. We derive simple equations of motion for the case of a two-component condensate that are identical to the extensively analyzed Bloch equations. We also find equilibrium points of the motion that are unstable in the spinless case.

•Jan 1, 2002•0 citations

Measurement theory for spinor condensates

Juha Javanainen

We study the experimental signatures of several states of a Bose-Einstein condensate of spin-1 atoms by quantum trajectory simulations of Stern-Gerlach experiments. The measurement process itself creates an apparent random alignment for the spins, so that it is difficult to distinguish between a condensate that initially has an alignment in an unknown direction and one with no alignment at all. Nonetheless, in repeated experiments with identically prepared condensates, it is possible to discriminate between certain ground states of the condensate proposed in the literature.

arXiv:cond-mat/0009089•Journal of Physics B Atomic Molecular and Optical Physics•Nov 28, 2000•7 citations

Interference of two Bose–Einstein condensates

Sung Mi Yoo, Janne Ruostekoski, Juha Javanainen

We show that, when two Bose-Einstein condensates are combined, a spatial interference pattern ensues even if the condensates are in number states with no spontaneously broken gauge symmetry. In our measurement-theoretical approach the interference pattern arises from correlations between the detected positions of the atoms. We also simulate numerically experiments intended to distinguish number-state condensates and spontaneous symmetry breaking, the latter being modelled by coherent-state condensates. To detect the difference in the pair correlation functions, the experiment has to be repeated about a thousand times even for condensates with as few as five atoms each.

Journal of Modern Optics•Oct 1, 1997•13 citations

Theoretical and experimental study of spin-1 antiferromagnetic Bose-Einstein Condensates

Shao, Lingxuan

In this thesis, we study theoretically and in experimentally the properties of spin-1 Bose-Einstein condensates with antiferromagnetic interactions realized in the ultra-cold sodium gases confined in optical dipole traps. We present in detail how to realize, diagnose and control the spinor Bose-Einstein condensates in our experiment. In order to describe the condensate, a mean-field theory is first adopted. This theory predicts a phase transition when changing the magnetic field $B$. The predictions of the mean-field theory agree very well with most of our experimental results, including the values of the critical magnetic field $B_c$, asymptotic values of $n_0$ (relative atom number in $m_F=0$ state) at large $B$ and the phase diagram of $n_0$. However, for small magnetization and small magnetic fields, we find abnormally large fluctuations (super-Poissonian) of $n_0$. In order to describe these large fluctuations, we develop a full quantum statistical description for the spinor condensate at finite temperature. To describe uncondensed thermal atoms (also present in the same trap), we use the ``semi-ideal" Hartree-Fock approximation to deal with the interactions between the condensate atoms and the thermal ones. The experimental results lead us to introduce two kinds of temperatures, the ``spin temperature" $T_s$ and the ``kinetic temperature" $T_k$ with $T_s\ll T_k$, characterizing respectively the fluctuaitons of the condensate spin and the thermal gas. We conclude that the system is reaching a quasi-equilibrium states, where different degrees of freedom reach equilibrium by separate mechanisms but where the mutual thermalization does not occur over the lifetime of the cloud.

•Jul 4, 2014•1 citation

Coherent Spin Dynamics of a Spin-1 Bose-Einstein Condensate

M.-S. Chang

Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.

•Apr 11, 2006•6 citations
We study two aspects of measurement theory in spinor Bose-Einstein condensates of F=1F=1F=1 atoms: the probability of obtaining a certain outcome of the measurement and the evolution of the state of the condensate due to the measurement. We also study the interference patterns arising from the spatial overlap of two spinor condensates. We show that neither a measurement on a small number of escaping atoms nor an interference experiment can distinguish between an antiferromagnetic coherent state condensate, i.e., a condensate in which all the atoms have Sz=0{S}_{z}=0Sz​=0 along an a priori unknown direction, and a spin-singlet condensate, i.e., a condensate with Stotal=0.{S}_{\mathrm{total}}=0.Stotal​=0. We also show that a singlet-state condensate evolves into a coherent state as a result of the measurement.
Abstract. We study the experimental signatures of several states of a Bose-Einstein condensate of spin-1 atoms by quantum trajectory simulations of Stern-Gerlach experiments. The measurement process itself creates an apparent random alignment for the spins, so that it is difficult to distinguish between a condensate that initially has an alignment in an unknown direction and one with no alignment at all. Nonetheless, in repeated experiments with identically prepared condensates, it is possible to discriminate between certain ground states of the condensate proposed in the literature. PACS numbers: 03.75.Fi,03.65.BzMeasurement theory for spinor condensates 2 1.
We study several problems in Bose-Einstein condensates with internal degrees of freedom, and we find that this kind of condensates, which are usually referred to as spinor condensates, exhibit several phenomena that are qualitatively different from scalar (i.e. spinless) condensates. We analyze the ground state of a condensate with the constraint of maintaining a constant value of the total spin, and we find a number of different structures depending on the value of the total spin and the applied external magnetic field. We also study a certain type of measurement on spinor condensates in an attempt to distinguish between the so-called coherent and singlet states. We find that this kind of measurement cannot distinguish between the two states in question. We then consider a different experiment based on the interference between spinor condensate. It turns out that interference experiments cannot be used to distinguish between coherent and singlet states either. One of the interesting results regarding interference between two spinor condensates is that both the offset and visibility of the interference fringes vary from shot to shot, even if the initial conditions are identical in all the runs of the experiment. We then turn to the problem of condensing a gas of effectively spin 1/2 atoms. We argue that if spin relaxation mechanisms are slow enough, the condensate displays the phenomenon of fragmentation. The main difference of the fragmented state that we study and other fragmented states discussed in the literature is that this one is not caused by interatomic interactions, but rather by the constraint on the total spin of the system. We investigate the consequences of performing the experiment in a toroidal trap, and we find that, under certain conditions, the system spontaneously builds up a macroscopic value of orbital angular momentum. We finally discuss several problems related to the external Josephson effect. We derive simple equations of motion for the case of a two-component condensate that are identical to the extensively analyzed Bloch equations. We also find equilibrium points of the motion that are unstable in the spinless case.
We study the experimental signatures of several states of a Bose-Einstein condensate of spin-1 atoms by quantum trajectory simulations of Stern-Gerlach experiments. The measurement process itself creates an apparent random alignment for the spins, so that it is difficult to distinguish between a condensate that initially has an alignment in an unknown direction and one with no alignment at all. Nonetheless, in repeated experiments with identically prepared condensates, it is possible to discriminate between certain ground states of the condensate proposed in the literature.
We show that, when two Bose-Einstein condensates are combined, a spatial interference pattern ensues even if the condensates are in number states with no spontaneously broken gauge symmetry. In our measurement-theoretical approach the interference pattern arises from correlations between the detected positions of the atoms. We also simulate numerically experiments intended to distinguish number-state condensates and spontaneous symmetry breaking, the latter being modelled by coherent-state condensates. To detect the difference in the pair correlation functions, the experiment has to be repeated about a thousand times even for condensates with as few as five atoms each.
In this thesis, we study theoretically and in experimentally the properties of spin-1 Bose-Einstein condensates with antiferromagnetic interactions realized in the ultra-cold sodium gases confined in optical dipole traps. We present in detail how to realize, diagnose and control the spinor Bose-Einstein condensates in our experiment. In order to describe the condensate, a mean-field theory is first adopted. This theory predicts a phase transition when changing the magnetic field BBB. The predictions of the mean-field theory agree very well with most of our experimental results, including the values of the critical magnetic field BcB_cBc​, asymptotic values of n0n_0n0​ (relative atom number in mF=0m_F=0mF​=0 state) at large BBB and the phase diagram of n0n_0n0​. However, for small magnetization and small magnetic fields, we find abnormally large fluctuations (super-Poissonian) of n0n_0n0​. In order to describe these large fluctuations, we develop a full quantum statistical description for the spinor condensate at finite temperature. To describe uncondensed thermal atoms (also present in the same trap), we use the ``semi-ideal" Hartree-Fock approximation to deal with the interactions between the condensate atoms and the thermal ones. The experimental results lead us to introduce two kinds of temperatures, the ``spin temperature" TsT_sTs​ and the ``kinetic temperature" TkT_kTk​ with Ts≪TkT_s\ll T_kTs​≪Tk​, characterizing respectively the fluctuaitons of the condensate spin and the thermal gas. We conclude that the system is reaching a quasi-equilibrium states, where different degrees of freedom reach equilibrium by separate mechanisms but where the mutual thermalization does not occur over the lifetime of the cloud.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.