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Phase Transitions in Engineered Ultracold Quantum Systems

Ryan Price

Published Jan 1, 2015• 0 citations
Publisher

Abstract

The study of quantum degenerate gases has many applications in topics such as condensed matter dynamics, precision measurements and quantum phase transitions. We built an apparatus to create 87Rb Bose-Einstein condensates (BECs) and generated, via optical and magnetic interactions, novel quantum systems in which we studied the contained phase transitions. For our first experiment we quenched multi-spin component BECs from a miscible to dynamically unstable immiscible state. The transition rapidly drives any spin fluctuations with a coherent growth process driving the formation of numerous spin polarized domains. At much longer times these domains coarsen as the system approaches equilibrium. For our second experiment we explored the magnetic phases present in a spin-1 spin-orbit coupled BEC and the contained quantum phase transitions. We observed ferromagnetic and unpolarized phases which are stabilized by the spin-orbit coupling’s explicit locking between spin and motion. These two phases are separated by a critical curve containing both first-order and second-order transitions joined at a critical point. The narrow first-order transition gives rise to long-lived metastable states. For our third experiment we prepared independent BECs in a double-well potential, with an artificial magnetic field between the BECs. We transitioned to a single BEC by lowering the barrier while expanding the region of artificial field to cover the resulting single BEC. We compared the vortex distribution nucleated via conventional dynamics to those produced by our procedure, showing our dynamical process populates vortices much more rapidly and in larger number than conventional nucleation.

DOI
10.13016/m2tr12

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The study of quantum degenerate gases has many applications in topics such as condensed matter dynamics, precision measurements and quantum phase transitions. We built an apparatus to create 87Rb Bose-Einstein condensates (BECs) and generated, via optical and magnetic interactions, novel quantum systems in which we studied the contained phase transitions. For our first experiment we quenched multi-spin component BECs from a miscible to dynamically unstable immiscible state. The transition rapidly drives any spin fluctuations with a coherent growth process driving the formation of numerous spin polarized domains. At much longer times these domains coarsen as the system approaches equilibrium. For our second experiment we explored the magnetic phases present in a spin-1 spin-orbit coupled BEC and the contained quantum phase transitions. We observed ferromagnetic and unpolarized phases which are stabilized by the spin-orbit coupling’s explicit locking between spin and motion. These two phases are separated by a critical curve containing both first-order and second-order transitions joined at a critical point. The narrow first-order transition gives rise to long-lived metastable states. For our third experiment we prepared independent BECs in a double-well potential, with an artificial magnetic field between the BECs. We transitioned to a single BEC by lowering the barrier while expanding the region of artificial field to cover the resulting single BEC. We compared the vortex distribution nucleated via conventional dynamics to those produced by our procedure, showing our dynamical process populates vortices much more rapidly and in larger number than conventional nucleation.
Phases of matter are characterized by order parameters describing the type and degree of order in a system. Here we experimentally explore the magnetic phases present in a near-zero temperature spin-1 spin-orbit-coupled atomic Bose gas and the quantum phase transitions between these phases. We observe ferromagnetic and unpolarized phases, which are stabilized by spin-orbit coupling's explicit locking between spin and motion. These phases are separated by a critical curve containing both first- and second-order transitions joined at a tricritical point. The first-order transition, with observed width as small as h × 4 Hz, gives rise to long-lived metastable states. These measurements are all in agreement with theory.
Abstract Phases of matter are characterized by order parameters describing the type and degree of order in a system. Here we experimentally explore the magnetic phases present in a near-zero temperature spin-1 spin–orbit-coupled atomic Bose gas and the quantum phase transitions between these phases. We observe ferromagnetic and unpolarized phases, which are stabilized by spin–orbit coupling’s explicit locking between spin and motion. These phases are separated by a critical curve containing both first- and second-order transitions joined at a tricritical point. The first-order transition, with observed width as small as h × 4 Hz, gives rise to long-lived metastable states. These measurements are all in agreement with theory.
We explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a U(1)\mathrm{U}(1)U(1) order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.
Bose-Einstein condensates (BECs) are a recent addition to the portfolio of quantum materials some of which have profound commercial and military applications e.g., superconductors, superfluids and light emitting diodes. BECs exist in the lowest motional modes of a trap and have the lowest temperatures achieved by mankind. With full control over the shape of the trap the experimentalist may explore an extremely diverse set of Hamiltonians which may be altered mid-experiment. These properties are particularly suited for realizing novel quantum systems. This thesis explores interaction-driven domain formation and the subsequent domain coarsening for two immiscible BEC components. Because quantum coherences associated with interactions in BECs can be derived from low energy scattering theory we compare our experimental results to both a careful simulation (performed by Brandon Anderson) and an analytical prediction. This result very carefully explores the question of how a metastable system relaxes at the extreme limit of low temperature. We also explore spin-orbit coupling (SOC) of a BEC which links the linear and discrete momentum transferable by two counterpropagating ``Raman'' lasers that resonantly couple the ground electronic states of our BECs. SOC is used similarly in condensed matter systems to describe coupling between charge carrier spin and crystal momentum and is a necessary component of the quantum spin Hall effect and topological insulators. SOC links the linear and discrete momentum transferable by two counterpropagating ``Raman'' lasers and a subset of the ground electronic states of our BEC. The phases of an effective 2-spin component spin-orbit coupling (SOC) in a spin-1 BEC are described in Lin et al. (2011). We measure the phase transition between two phases of a spin-1 BEC with SOC which cannot be mimicked by a spin-1/2 system. The order parameter that describes transitions between these two phases is insensitive to magnetic field fluctuations. I also describe a realistic implementation of Rashba SOC. This type of SOC is expected to exhibit novel many-body phases [Stanescu et al. 2008, Sedrakyan et al. 2012, Hu et al. 2011].
Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.
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.