Spin-changing Collisions Research Articles

Dynamics of a pair of overlapping polar bright solitons in spin-1 Bose-Einstein condensates

We analyze the dynamics of both population and spin densities, emerging from the spatial overlap between two distinct polar bright solitons in Spin-1 Spinor Condensates. The dynamics of overlapping solitons in scalar condensates exhibits soliton fusion, atomic switching from one soliton to another and repulsive dynamics depending on the extent of overlap and the relative phase between the solitons. The scalar case also helps us understand the dynamics of the vector solitons. In the spinor case, non-trivial dynamics emerge in spatial and spin degrees of freedom. In the absence of spin changing collisions, we observe Josephson-like oscillations in the population dynamics of each spin component. In this case, the population dynamics is independent of the relative phase, but the dynamics of the spin-density vector depends on it. The latter also witnesses the appearance of oscillating domain walls. The pair of overlapping polar solitons emerge as four ferromagnetic solitons irrespective of the initial phase difference for identical spin-dependent and spin-independent interaction strengths. But the dynamics of final solitons depends explicitly on the relative phase. Depending on the ratio of spin-dependent and spin-independent interaction strengths, a pair of oscillatons can also emerge as the final state. Then, increasing the extent of overlap may lead to the simultaneous formation of both a stationary ferromagnetic soltion and a pair of oscillatons depending on the relative phase.

Bell correlations in a split two-mode-squeezed Bose-Einstein condensate

We propose and analyze a protocol for observing a violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality using two spatially separated Bose-Einstein condensates (BECs). To prepare the Bell-correlated state, spin-changing collisions are used to first prepare a two-mode squeezed BEC. This is then split into two BECs by controlling the spatial wavefunction, e.g., by modifying the trapping potential. Finally, spin-changing collisions are also exploited locally, to compensate local squeezing terms. The correlators appearing in the inequality are evaluated using three different approaches. In the first approach, correlators are estimated using normalized expectation values of number operators, in a similar way to evaluating continuous-variable Bell inequalities. An improvement to this approach is developed using the sign-binning of total spin measurements, which allows for the construction of two-outcome measurements and violations of the CHSH inequality without auxiliary assumptions. Finally, we show a third approach where maximal violations of the CH inequality can be obtained by assigning zero values to local vacua outcomes under a no-enhancement assumption. The effect of loss and imperfect detection efficiency is investigated and the observed violations are found to be robust to noise.

Tailored generation of quantum states in an entangled spinor interferometer to overcome detection noise

We theoretically investigate how entangled atomic states generated via spin-changing collisions in a spinor Bose-Einstein condensate can be designed and controllably prepared for atom interferometry that is robust against common technical issues, such as limited detector resolution. We use analytic and numerical treatments of the spin-changing collision process to demonstrate that triggering the entangling collisions with a small classical seed rather than vacuum fluctuations leads to a more robust and superior sensitivity when technical noise is accounted for, despite the generated atomic state ideally featuring less metrologically useful entanglement. Our results are relevant for understanding how entangled atomic states are best designed and generated for use in quantum-enhanced matter-wave interferometry.

Scalable Cold-Atom Quantum Simulator for Two-Dimensional QED.

We propose a scalable analog quantum simulator for quantum electrodynamics in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs interspecies spin-changing collisions in an ultracold atomic mixture trapped in an optical lattice. We engineer spatial plaquette terms for magnetic fields, thus solving a major obstacle toward experimental realizations of realistic gauge theories in higher dimensions. We apply our approach to the pure gauge theory of compact QED and discuss how the phenomenon of confinement of electric charges can be described by the quantum simulator.

Dynamical preparation of stripe states in spin-orbit-coupled gases

In spinor Bose-Einstein condensates, spin-changing collisions are a remarkable proxy to coherently realize macroscopic many-body quantum states. These processes have been, e.g., exploited to generate entanglement, to study dynamical quantum phase transitions, and proposed for realizing nematic phases in atomic condensates. In the same systems dressed by Raman beams, the coupling between spin and momentum induces a spin dependence in the scattering processes taking place in the gas. Here we show that, at weak couplings, such modulation of the collisions leads to an effective Hamiltonian which is equivalent to the one of an artificial spinor gas with spin-changing collisions that are tunable with the Raman intensity. By exploiting this dressed-basis description, we propose a robust protocol to coherently drive the spin-orbit coupled condensate into the ferromagnetic stripe phase via crossing a quantum phase transition of the effective low-energy model in an excited-state.

Integrable active atom interferometry

Active interferometers are designed to enhance phase sensitivity beyond the standard quantum limit by generating entanglement inside the interferometer. An atomic version of such a device can be constructed by means of a spinor Bose–Einstein condensate with an F = 1 groundstate manifold in which spin-changing collisions (SCCs) create entangled pairs of m = ±1 atoms. We use Bethe Ansatz techniques to find exact eigenstates and eigenvalues of the Hamiltonian that models such SCCs. Using these results, we express the interferometer’s phase sensitivity, Fisher information, and Hellinger distance in terms of the Bethe rapidities. By evaluating these expressions we study scaling properties and the interferometer’s performance under the full Hamiltonian that models the SCCs, i.e., without the idealising approximations of earlier works that force the model into the framework of SU(1,1) interferometry.

Collisional spin transfer in an atomic heteronuclear spinor Bose gas

We observe spin transfer within a non-degenerate heteronuclear spinor atomic gas comprised of a small $^7$Li population admixed with a $^{87}$Rb bath, with both elements in their $F=1$ hyperfine spin manifolds and at temperatures of 10's of $\mu$K. Prepared in a non-equilibrium initial state, the $^7$Li spin distribution evolves through incoherent spin-changing collisions toward a steady-state distribution. We identify and measure the cross-sections of all three types of spin-dependent heteronuclear collisions, namely the spin-exchange, spin-mixing, and quadrupole-exchange interactions, and find agreement with predictions of heteronuclear $^7$Li-$^{87}$Rb interactions at low energy. Moreover, we observe that the steady state of the $^7$Li spinor gas can be controlled by varying the composition of the $^{87}$Rb spin bath with which it interacts.

Probing Spin Correlations in a Bose-Einstein Condensate Near the Single-Atom Level.

Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3dB.

Suppression and control of prethermalization in multicomponent Fermi gases following a quantum quench

We investigate the mechanisms of control and suppression of pre-thermalization in $N$-component alkaline earth gases. To this end, we compute the short-time dynamics of the instantaneous momentum distribution and the relative population for different initial conditions after an interaction quench, accounting for the 11 peffect of initial interactions. We find that switching on an interaction that breaks the SU$(N)$ symmetry of the initial Hamiltonian, thus allowing for the occurrence of spin-changing collisions, does not necessarily lead to a suppression of pre-thermalization. However, the suppression will be most effective in the presence of SU$(N)$-breaking interactions provided the number of components $N \ge 4$ and the initial state contains a population imbalance that breaks the SU$(N)$ symmetry. We also find the conditions on the imbalance initial state that allow for a pre-thermal state to be stabilized for a certain time. Our study highlights the important role played by the initial state in the pre-thermalization dynamics of multicomponent Fermi gases. It also demonstrates that alkaline-earth Fermi gases provide an interesting playground for the study and control of pre-thermalization.

Gauge invariance with cold atoms

Quantum Simulation There is considerable interest in developing quantum computational technologies that can simulate a series of physical phenomena inaccessible by classical computers. Mil et al. propose a modular scheme for quantum simulation of a U(1) lattice gauge theory based on heteronuclear spin-changing collisions in a mixture of two bosonic quantum gases isolated in single wells of a one-dimensional optical lattice. They engineered the elementary building block for a single well and demonstrate its reliable operation that preserves the gauge invariance. The potential for scalability of the proposed scheme opens up opportunities to address challenges in quantum simulating the continuum limit of the gauge theories. Science , this issue p. [1128][1] [1]: /lookup/doi/10.1126/science.aaz5312

A scalable realization of local U(1) gauge invariance in cold atomic mixtures.

In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.

Quantum Rydberg Central Spin Model.

We consider dynamics of a Rydberg impurity in a cloud of ultracold bosonic atoms in which the Rydberg electron undergoes spin-changing collisions with surrounding atoms. This system realizes a new type of quantum impurity problems that compounds essential features of the Kondo model, the Bose polaron, and the central spin model. To capture the interplay of the Rydberg-electron spin dynamics and the orbital motion of atoms, we employ a new variational method that combines an impurity-decoupling transformation with a Gaussian ansatz for the bath particles. We find several unexpected features of this model that are not present in traditional impurity problems, including interaction-induced renormalization of the absorption spectrum that eludes simple explanations from molecular bound states, and long-lasting oscillations of the Rydberg-electron spin. We discuss generalizations of our analysis to other systems in atomic physics and quantum chemistry, where an electron excitation of high orbital quantum number interacts with a spinful quantum bath.

Efficient variational approach to dynamics of a spatially extended bosonic Kondo model

We develop an efficient variational approach to studying dynamics of a localized quantum spin coupled to a bath of mobile spinful bosons. We use parity symmetry to decouple the impurity spin from the environment via a canonical transformation and reduce the problem to a model of the interacting bosonic bath. We describe coherent time evolution of the latter using bosonic Gaussian states as a variational ansatz. We provide full analytical expressions for equations describing variational time evolution that can be applied to study in- and out-of-equilibrium phenomena in a wide class of quantum impurity problems. In the accompanying paper [Y. Ashida {\it et al.}, Phys. Rev. Lett. 123, 183001 (2019)], we present a concrete application of this general formalism to the analysis of the Rydberg Central Spin Model, in which the spin-1/2 Rydberg impurity undergoes spin-changing collisions in a dense cloud of two-component ultracold bosons. To illustrate new features arising from orbital motion of the bath atoms, we compare our results to the Monte Carlo study of the model with spatially localized bosons in the bath, in which random positions of the atoms give rise to random couplings of the standard central spin model.

Spinor Bose-Einstein condensate interferometer within the undepleted pump approximation: Role of the initial state

Most interferometers operate with photons or dilute, non-condensed cold atom clouds in which collisions are strongly suppressed. Spinor Bose-Einstein condensates (BECs) provide an alternative route toward realizing three-mode interferometers; in this realization, spin-changing collisions provide a resource that generates mode entanglement. Working in the regime where the pump mode, i.e., the m=0 hyperfine state, has a much larger population than the side or probe modes (m=+1 and m=-1 hyperfine states), f=1 spinor BECs approximate SU(1,1) interferometers. We derive analytical expressions within the undepleted pump approximation for the phase sensitivity of such an SU(1,1) interferometer for two classes of initial states: pure Fock states and coherent spin states. The interferometer performance is analyzed for initial states without seeding, with single-sided seeding, and with double-sided seeding. The validity regime of the undepleted pump approximation is assessed by performing quantum calculations for the full spin Hamiltonian. Our analytical results and the associated dynamics are expected to guide experiments as well as numerical studies that explore regimes where the undepleted pump approximation makes quantitatively or qualitatively incorrect predictions.

ZN gauge theories coupled to topological fermions: QED2 with a quantum mechanical θ angle

We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes (1+1) quantum electrodynamics of an Abelian $U(1)$ gauge field coupled to a symmetry-protected topological matter sector, by means of a class of $\mathbb{Z}_N$ lattice gauge theories. Employing density-matrix renormalization group techniques that exactly implement Gauss' law, we show that these models host a correlated topological phase for different values of $N$, where fermion correlations arise through inter-particle interactions mediated by the gauge field. Moreover, by a careful finite-size scaling, we show that this phase is stable in the large-$N$ limit, and that the phase boundaries are in accordance to bosonization predictions of the $U(1)$ topological Schwinger model. Our results demonstrate that $\mathbb{Z}_N$ finite-dimensional gauge groups offer a practical route for an efficient classical simulation of equilibrium properties of electromagnetism with topological fermions. Additionally, we describe a scheme for the quantum simulation of a topological Schwinger model exploiting spin-changing collisions in boson-fermion mixtures of ultra-cold atoms in optical lattices. Although technically challenging, this quantum simulation would provide an alternative to classical density-matrix renormalization group techniques, providing also an efficient route to explore real-time non-equilibrium phenomena.

Microwave preparation of two-dimensional fermionic spin mixtures

We present a method for preparing a single two-dimensional sample of a two-spin mixture of fermionic potassium in a single antinode of an optical lattice, in a quantum-gas microscope apparatus. Our technique relies on spatially-selective microwave transitions in a magnetic field gradient. Adiabatic transfer pulses were optimized for high efficiency and minimal atom loss and heating due to spin-changing collisions. We have measured the dynamics of those loss processes, which are more pronounced in the presence of a spin mixture. As the efficient preparation of atoms in a single antinode requires a homogeneous transverse magnetic field, we developed a method to image and minimize the magnetic field gradients in the focal plane of the microscope.

Imaging ion-molecule reactions: Charge transfer and halide transfer reactions of O+ with CH3Cl, CH3Br, and CH3I

Velocity map images have been recorded for the charge transfer reactions of O+(4S) with CH3Cl, CH3Br, and CH3I at collision energies near 4eV. The production of methyl halide cations occurs for all systems, with relative abundances ranging from 10 to 15% of the total reaction yield. In addition, small yields of the dissociative charge transfer products Br+ and I+ are observed. The velocity space images show that charge transfer is energy resonant, and occurs by long range electron transfer. The predominant product in all three systems is CH3+, which may form by dissociation of the nascent CH3X+ product on a quartet potential energy surface, or by halide ion abstraction from CH3X by O+ following a spin-changing transition from the initial quartet surface to a doublet surface. The kinetic energy distributions for CH3+ formation show both a sharp low energy feature that appears to describe the formation of CH3++O(3P)+X(2P), in addition to a higher energy component that describes the more exoergic channel forming CH3++XO(2Π). The relative intensity of this high energy feature increases as the halogen atom X changes from Cl to Br to I, a progression that correlates with the strength of the halogen atom spin–orbit splitting. This observation supports the conclusion that the formation of the CH3+ products via the most exoergic channels, i.e., CH3++XO(2Π), does occur through spin-changing collisions from quartet to doublet state surfaces that are mediated by spin–orbit coupling.

Spin dynamics in a two-dimensional quantum gas

We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimposed angular density modulations. The density distributions depend on the applied magnetic field and are well explained by a simple Bogoliubov model. We show that the two clouds are anticorrelated in momentum space. The observed momentum correlations pave the way towards the creation of an atom source with nonlocal Einstein-Podolsky-Rosen entanglement.

Large-amplitude superexchange of high-spin fermions in optical lattices

We show that fermionic high-spin systems with spin-changing collisions allow one to monitor superexchange processes in optical superlattices with large amplitudes and strong spin fluctuations. By investigating the non-equilibrium dynamics, we find a superexchange dominated regime at weak interactions. The underlying mechanism is driven by an emerging tunneling-energy gap in shallow few-well potentials. As a consequence, the interaction-energy gap that is expected to occur only for strong interactions in deep lattices is re-established. By tuning the optical lattice depth, a crossover between two regimes with negligible particle number fluctuations is found: firstly, the common regime with vanishing spin-fluctuations in deep lattices and, secondly, a novel regime with strong spin fluctuations in shallow lattices. We discuss the possible experimental realization with ultracold 40K atoms and observable quantities in double wells and two-dimensional plaquettes.

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

Under the influence of an external magnetic field and spin-changing collisions, the band insulator (BI) state of one-dimensional (1D) s-wave repulsively interacting 4-component fermions at half-filling transforms into Mott insulator (MI) states with spontaneously broken translational symmetry: a dimerized state for shallow lattices and a N{\'e}el state for deep lattices via an intermediate topological state. Since a BI has vanishing entropy per particle, these MI phases could be particularly inviting for experimental realization under the similar conditions as those for $^{40}$K atoms [1], provided the magnetic field is changed adiabatically.