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

Measurement theory for spinor condensates

Juha Javanainen

Published Jan 1, 2000• 3 citations
OpenAlex

Abstract

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.

Related papers

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

Measurement theory and interference of spinor Bose-Einstein condensates

Sahel Ashhab, A. J. Leggett

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.

Physical Review A•Jan 17, 2002•21 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

Stern-Gerlach entanglement in spinor Bose-Einstein condensates

Sara Cruz-Barrios, Maria Carolina Nemes, A. F. R. de Toledo Piza

Entanglement of spin and position variables produced by spatially inhomogeneous magnetic fields of Stern-Gerlach type acting on spinor Bose-Einstein condensates may lead to interference effects at the level of one-boson densities. A model is worked out for these effects which is amenable to analytical calculation for gaussian shaped condensates. The resulting interference effects are sensitive to the spin polarization properties of the condensate.

arXiv:cond-mat/0202055•Europhysics Letters (EPL)•Jan 1, 2003•2 citations

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

Effective non-linear spinor dynamics in a spin-1 Bose–Einstein condensate

Alessandro Michelangeli, Alessandro Olgiati

Abstract We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.

arXiv:1803.05410•Journal of Physics A Mathematical and Theoretical•Aug 21, 2018•2 citations
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 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 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.
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.
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.
Abstract We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.