Scaling of Fluctuations in a Trapped Binary Condensate

Abstract

We demonstrate that measurements of number fluctuations within finite cells provide a direct means to study fluctuation scaling in a trapped two-component condensate. This quantum system supports a second-order phase transition between miscible (co-spatial) and immiscible (symmetry-broken) states that is driven by a diverging susceptibility to magnetic fluctuations. As the transition is approached from the miscible side the magnetic susceptibility is found to depend strongly on the geometry and orientation of the observation cell. However, a scaling exponent consistent with that for the homogenous gas ($\gamma =1$) can be recovered, for all cells considered, as long as the fit excludes the region in the immediate vicinity of the critical point. As the transition is approached from the immiscible side, the magnetic fluctuations exhibit a non-trivial scaling exponent $\gamma \simeq 1.30$. Experimentally, the observation cells may be formed either by considering individual imaging pixels or by combining pixels to form larger cells, and fluctuation statistics can be obtained by repeated \emph{in situ} images. Interestingly, on both sides of the transition, we find it best to extract the exponents using an observation cell that covers half of the trapped system. This implies that relatively low-resolution \emph{in situ} imaging will be adequate for the investigation of these exponents. We also investigate the gap energy and find exponents $\nu z$ = 0.505 on the miscible side and, unexpectedly, $\nu z$ = 0.60(3) for the immiscible phase.

7 pages, 3 figures

References in corpus (14)

• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Roton-type mode softening in a quantum gas with cavity-mediated long-range interactions
• Observation of scale invariance and universality in two-dimensional Bose gases
• Dual-Species Bose-Einstein Condensate of ${}^{87}$Rb and ${}^{133}$Cs
• Spatially inhomogeneous phase evolution of a two-component Bose-Einstein condensate
• Equilibrium solutions of immiscible two-species Bose-Einstein condensates in perturbed harmonic traps
• Can a Bose gas be saturated?
• Dynamical pattern formation during growth of a dual-species Bose-Einstein condensate
• N-conserving Bogoliubov vacuum of a two component Bose-Einstein condensate: Density fluctuations close to a phase separation condition
• Dispersion relation and excitation character of a two-component Bose-Einstein condensate
• The Miscible-Immiscible Quantum Phase Transition in Coupled Two-Component Bose-Einstein Condensates in 1D Optical Lattices
• Fluctuation and interaction induced instability of dark solitons in single and binary condensates
• Fluctuations of spinor Bose-Einstein condensates
• Spin critical opalescence in zero temperature Bose-Einstein Condensates

Cited by in corpus (1)

• Spin-Dipole Oscillation and Polarizability of a Binary Bose-Einstein Condensate near the Miscible-Immiscible Phase Transition