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arXiv:cond-mat/0009089 · Journal of Physics B Atomic Molecular and Optical Physics

Measurement theory for spinor condensates

Juha Javanainen

Published Nov 28, 2000• 7 citations
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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.

DOI
10.1088/0953-4075/33/24/303

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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.
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 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.
This thesis is devoted to the construction, optimization and characterization of an experimental apparatus, capable of creating spinor condensates of ~1x10^5 atoms with a repetition rate of 10s, using an all-optical evaporation technique. I report a complete description of the experimental apparatus and techniques used in the experiment and a characterization of the BEC sample. We study the transmission of absorption imaging pictures through a coherent fiber bundle. We show that the fiber bundle introduces spurious noise in the picture mainly due to the strong core-to-core coupling. We demonstrate that we can retrieve exact quantitative information about the atomic system using this technique. We also explore the equilibration dynamics of ferromagnetic spin-1 system as a function of the initial magnetization of the sample and the external magnetic field. We show that the magnetization of the system is conserved despite of the presence of dissipative processes that are intrinsic to any experiment. We investigated the formation of the BEC in a spin-1 quantum gas in the presence of an external magnetic field. We report on the spontaneous magnetization of the condensate fraction during the evaporation process at low magnetic fields. We as well observe multi-step condensation, and found signatures of a possible interspecies Feshbach resonance.
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.