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MAGNETIZED PLANE WAVE AND STRIPE-ORDERED PHASES IN SPIN-ORBIT-COUPLED BOSE GASES

Andika Putra

Published Jan 1, 2018• 0 citations
Publisher

Abstract

Quantum degenerate gases have provided rich systems to simulate engineered Hamiltonians and to explore quantum many-body problems in laboratory-scale experiments. In this work, I focus on spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) of Rubidium-87 atoms realized using two-photon Raman coupling in which various novel phases are predicted to exist due to competing energies from the atomic internal structure, coupling strength, and many-body collisions. BECs are observed primarily using the interaction between light and matter, where it is common to probe the atoms with near-resonant light and image their shadow on a camera. This absorption imaging technique measures the integrated column density of the atoms and it is crucial to focus the imaging system. I present a systematic method to bring the ultracold atom systems into an optimal focus using the power spectral density (PSD) of the atomic density-density correlation function. The spatial frequency at which the defocus-induced artifacts first appear in the PSD is maximized at the focus. The focusing process thus identifies the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects. Next, I describe magnetic phases which exist in spin-1 spin-orbit-coupled condensates at a near-zero temperature. I observe ferromagnetic and unmagnetized phases which are stabilized by the locking between the spin and linear momentum of the system. Our measurements of both the first- and second-order transitions are in agreement with theory. Finally, I discuss the stripe-ordered phase that occurs in SOC Bose gases favoring the miscibility configuration. The stripe phase is theoretically predicted to have an excitation spectrum analogous to that of a supersolid and to exhibit spatial density modulation within specific regions of parameter space. I used optical Bragg scattering to probe the small density modulation present in the atomic spatial distribution. I present for the very first time observation of the stripe phase in a Raman SOC Bose gas and its phase diagram in various parameter space. Our observations of the phase boundaries are consistent with theory and previous work.

DOI
10.13016/m2125qd0m

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Quantum degenerate gases have provided rich systems to simulate engineered Hamiltonians and to explore quantum many-body problems in laboratory-scale experiments. In this work, I focus on spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) of Rubidium-87 atoms realized using two-photon Raman coupling in which various novel phases are predicted to exist due to competing energies from the atomic internal structure, coupling strength, and many-body collisions. BECs are observed primarily using the interaction between light and matter, where it is common to probe the atoms with near-resonant light and image their shadow on a camera. This absorption imaging technique measures the integrated column density of the atoms and it is crucial to focus the imaging system. I present a systematic method to bring the ultracold atom systems into an optimal focus using the power spectral density (PSD) of the atomic density-density correlation function. The spatial frequency at which the defocus-induced artifacts first appear in the PSD is maximized at the focus. The focusing process thus identifies the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects. Next, I describe magnetic phases which exist in spin-1 spin-orbit-coupled condensates at a near-zero temperature. I observe ferromagnetic and unmagnetized phases which are stabilized by the locking between the spin and linear momentum of the system. Our measurements of both the first- and second-order transitions are in agreement with theory. Finally, I discuss the stripe-ordered phase that occurs in SOC Bose gases favoring the miscibility configuration. The stripe phase is theoretically predicted to have an excitation spectrum analogous to that of a supersolid and to exhibit spatial density modulation within specific regions of parameter space. I used optical Bragg scattering to probe the small density modulation present in the atomic spatial distribution. I present for the very first time observation of the stripe phase in a Raman SOC Bose gas and its phase diagram in various parameter space. Our observations of the phase boundaries are consistent with theory and previous work.
Spin-orbit-coupled Bose-Einstein condensates (SOBECs) exhibit two new phases of matter, now known as the stripe and plane-wave phases. When two interacting spin components of a SOBEC spatially overlap, density modulations with periodicity given by the spin-orbit coupling strength appear. In equilibrium, these components fully overlap in the miscible stripe phase and overlap only in a domain wall in the immiscible plane-wave phase. Here we probe the density modulation present in any overlapping region with optical Bragg scattering and observe the sudden drop of Bragg scattering as the overlapping region shrinks. Using an atomic analog of the Talbot effect, we demonstrate the existence of long-range coherence between the different spin components in the stripe phase and surprisingly even in the phase-separated plane-wave phase.
Excited-state quantum phase transitions depend on and reveal the structure of the whole spectrum of many-body systems. While they are theoretically well understood, finding suitable signatures and detecting them in actual experiments remains challenging. For instance, in spinor gases, excited-state phases have been identified and characterized through a topological order parameter that is challenging to measure in experiments. Here we propose the Raman-dressed spin-orbit-coupled gas as a novel platform to explore excited-state quantum phase transitions. In a weakly coupled regime, the dressed system is equivalent to a spinor gas with tunable spin-spin interactions. Through this equivalence we are able to identify excited-state phases in the Raman-dressed Bose gas. The phases are characterized by the behavior of the spatial density modulations, or stripes, induced by spin-orbit coupling, and can in principle be measured in current state-of-the-art experiments with ultracold atoms. Conversely, we show that the properties of the excited phase can be exploited to prepare stripe states with large and stable density modulations.
We study the ground-state phase diagram and the quantum phase transitions in spin-1 Bose gases with Raman-induced spin-orbit coupling. In addition to the Bose-Einstein condensates with uniform density, three types of stripe condensation phases that simultaneously break the U(1) symmetry and the translation symmetry are identified. The transitions between these phases are investigated, and the occurrences of the various tricritical points are predicted. The excitation spectra in the plane-wave phase and the zero-momentum phase show rich roton-maxon structures, and their instabilities indicate the tendency to develop the crystalline order. We propose the atomic gas of 23Na^{23}\mathrm{Na}23Na could be a candidate for observing the stripe condensate with high contrast fringes.
In this paper, we study-induced spin–orbit coupling (SOC) in one-dimensional ultracold quantum gases composed of atoms of different species. One species is subjected to an equal combination of Rashba and Dresselhaus SOC generated by Raman transition. The two species interact with each other through spin-independent and spin-exchange contact interactions. The spin-exchange interaction introduces a locking pattern of the momentum and spin degrees of freedom for the species without direct SOC. For small spin-independent interactions, the two species overlap and the induced SOC is effective. For large spin-independent interactions, however, the two species keep separate from each other and the induced SOC is negligible. We propose to generate inhomogeneous SOC by exploiting density engineering technique applied to the directly spin–orbit coupled Bose–Einstein condensate. When the effective potential is of Gaussian type, the single-particle eigenenergies and eigenstates are calculated by exact diagonalization method. For general cases, mean-field ground states are obtained by numerically searching for the minimum of energy functional. With the density engineering technique, it is possible to produce hybrid structures of plane wave, stripe and/or zero-momentum phases.
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].
The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this review we explore the properties of a spin-orbit-coupled Bose-Einstein condensate with equal Rashba and Dresselhaus strengths. This system presents a rich phase diagram, which exhibits a tricritical point separating a zero-momentum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.