Synthetic Spin-orbit Coupling Research Articles

Satyendra Nath Bose: quantum statistics to Bose-Einstein condensation

Satyendra Nath (S.N.) Bose is one of the great Indian scientists. His remarkable work on the black body radiation or derivation of Planck’s law led to quantum statistics, in particular, the statistics of photon. Albert Einstein applied Bose’s idea to a gas made of atoms and predicted a new state of matter now called Bose-Einstein condensate. It took 70 years to observe the predicted condensation phenomenon in the laboratory. With a brief introduction to the formative period of Professor Bose, this research survey begins with the founding works on quantum statistics and, subsequently, provides a brief account of the series of events terminating in the experimental realization of Bose-Einstein condensation. We also provide two simple examples to visualize the role of synthetic spin-orbit coupling in a quasi-one-dimensional condensate with attractive atom-atom interaction.

Electrical manipulation of a single electron spin in CMOS using a micromagnet and spin-valley coupling

For semiconductor spin qubits, complementary-metal-oxide-semiconductor (CMOS) technology is a promising candidate for reliable and scalable fabrication. Making the direct leap from academic fabrication to qubits fully fabricated by industrial CMOS standards is difficult without intermediate solutions. With a flexible back-end-of-line (BEOL), functionalities such as micromagnets or superconducting circuits can be added in a post-CMOS process to study the physics of these devices or achieve proofs-of-concept. Once the process is established, it can be incorporated in the foundry-compatible process flow. Here, we study a single electron spin qubit in a CMOS device with a micromagnet integrated in the flexible BEOL. We exploit the synthetic spin orbit coupling (SOC) to control the qubit via electric fields and we investigate the spin-valley physics in the presence of SOC where we show an enhancement of the Rabi frequency at the spin-valley hotspot. Finally, we probe the high frequency noise in the system using dynamical decoupling pulse sequences and demonstrate that charge noise dominates the qubit decoherence in this range.

Spin-orbit enhancement in Si/SiGe heterostructures with oscillating Ge concentration

Electrons in Si/SiGe quantum dots are a promising platform for quantum computation. Many leading designs, however, rely on synthetic spin-orbit coupling arising from micromagnets, leading to challenges in scaling. Here, it is shown that the intrinsic spin-orbit coupling of the conduction-band valleys can be enhanced by over an order of magnitude by including Ge concentration oscillations of an appropriate wavelength within the quantum-well region. This enables fast spin manipulation using electric dipole spin resonance in the absence of micromagnets.

Correlated Chern insulators in two-dimensional Raman lattices: A cold-atom regularization of strongly coupled four-Fermi field theories

We show that synthetic spin-orbit coupling for ultracold atoms in optical Raman potentials can be exploited to build versatile quantum simulators of correlated Chern insulators connected to strongly coupled four-Fermi field theories similar to the Gross-Neveu model in (2+1) dimensions. Exploiting this multidisciplinary perspective, we identify a large-N quantum anomalous Hall (QAH) effect in absence of any external magnetic field, and use it to delimit regions in parameter space where these correlated topological phases appear, the boundaries of which are controlled by strongly coupled fixed points of these four-Fermi relativistic field theories. We further show how, for strong interactions, the QAH effect gives way to magnetic phases described by a two-dimensional quantum compass model in a transverse field. We present a detailed description of the phase diagram using the large-N effective potential, and variational techniques such as projected entangled pairs.Received 22 December 2020Revised 8 July 2022Accepted 25 July 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L042012Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChern insulatorsLattice field theoryOptical lattices & trapsQuantum simulationAtomic, Molecular & OpticalQuantum InformationCondensed Matter, Materials & Applied Physics

A single hole spin with enhanced coherence in natural silicon

Semiconductor spin qubits based on spin–orbit states are responsive to electric field excitations, allowing for practical, fast and potentially scalable qubit control. Spin electric susceptibility, however, renders these qubits generally vulnerable to electrical noise, which limits their coherence time. Here we report on a spin–orbit qubit consisting of a single hole electrostatically confined in a natural silicon metal-oxide-semiconductor device. By varying the magnetic field orientation, we reveal the existence of operation sweet spots where the impact of charge noise is minimized while preserving an efficient electric-dipole spin control. We correspondingly observe an extension of the Hahn-echo coherence time up to 88 μs, exceeding by an order of magnitude existing values reported for hole spin qubits, and approaching the state-of-the-art for electron spin qubits with synthetic spin–orbit coupling in isotopically purified silicon. Our finding enhances the prospects of silicon-based hole spin qubits for scalable quantum information processing.

Large-S and Tensor-Network Methods for Strongly-Interacting Topological Insulators

The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain lattice Hubbard models of topological insulators, which map onto four-Fermi quantum field theories with a Wilson-type discretisation and have been recently shown to be at reach of cold-atom quantum simulators based on synthetic spin-orbit coupling. We combine large-S and tensor-network techniques to explore the possible spontaneous symmetry-breaking phases that appear when the interactions of the topological insulators are sufficiently large. In particular, we show that varying the Wilson parameter r of the lattice discretisations leads to a novel Heisenberg–Ising compass model with critical lines that flow with the value of r.

Variability of Electron and Hole Spin Qubits Due to Interface Roughness and Charge Traps

Semiconductor spin qubits may show significant device-to-device variability in the presence of spin-orbit coupling mechanisms. Interface roughness, charge traps, layout or process inhomogeneities indeed shape the real space wave functions, hence the spin properties. It is, therefore, important to understand how reproducible the qubits can be, in order to assess strategies to cope with variability, and to set constraints on the quality of materials and fabrication. Here we model the variability of single qubit properties (Larmor and Rabi frequencies) due to disorder at the Si/SiO$_2$ interface (roughness, charge traps) in metal-oxide-semiconductor devices. We consider both electron qubits (with synthetic spin-orbit coupling fields created by micro-magnets) and hole qubits (with intrinsic spin-orbit coupling). We show that charge traps are much more limiting than interface roughness, and can scatter Rabi frequencies over one order of magnitude. We discuss the implications for the design of spin qubits and for the choice of materials.

Large-[formula omitted] Chern insulators: Lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect

Four-Fermi quantum field theories in (2+1) dimensions lie among the simplest models in high-energy physics, the understanding of which requires a non-perturbative lattice formulation addressing their strongly-coupled fixed points. These lattice models are also relevant in condensed matter, as they offer a neat playground to explore strong correlations in the quantum anomalous Hall (QAH) effect. We give a detailed description of our multidisciplinary approach to understand the fate of the QAH phases as the four-Fermi interactions are increased, which combines strong-coupling and effective-potential techniques, unveiling a rich phase diagram with large-N Chern insulators and Lorentz-breaking fermion condensates. Moreover, this toolbox can be enlarged with recent advances in quantum information science, as we show that tensor-network algorithms based on projected entangled pairs can be used to improve our understanding of the strong-coupling limit. We also present a detailed scheme that uses ultra-cold atoms in optical lattices with synthetic spin–orbit coupling to build quantum simulators of these four-Fermi models. This yields a promising alternative to characterize the strongly-coupled fixed points and, moreover, could also explore real-time dynamics and finite-fermion densities.

Spin manipulation and decoherence in a quantum dot mediated by a synthetic spin–orbit coupling of broken T-symmetry

The electrical control of a spin qubit in a quantum dot (QD) relies on spin–orbit coupling (SOC), which could be either intrinsic to the underlying crystal lattice or heterostructure, or extrinsic via, for example, a micro-magnet. In experiments, micromagnets have been used as a synthetic SOC to enable strong coupling of a spin qubit in quantum dots with electric fields. Here we study theoretically the spin relaxation, pure dephasing, spin manipulation, and spin–photon coupling of an electron in a QD due to the synthetic SOC induced spin–orbit mixing. We find qualitative difference in the spin dynamics in the presence of a synthetic SOC compared with the case of the intrinsic SOC. Specifically, spin relaxation due to the synthetic SOC and deformation potential phonon emission (or Johnson noise) shows (or B 0) dependence with the magnetic field, which is in contrast with the (or ) dependence in the case of the intrinsic SOC. Moreover, charge noise induces fast spin dephasing to the first order of the synthetic SOC, which is in sharp contrast with the negligible spin pure dephasing in the case of the intrinsic SOC. These qualitative differences are attributed to the broken time-reversal symmetry (T-symmetry) of the synthetic SOC. An SOC with broken T-symmetry (such as the synthetic SOC from a micro-magnet) eliminates the ‘Van Vleck cancellation’ and causes a finite longitudinal spin–electric coupling that allows the longitudinal coupling between spin and electric field, and in turn allows spin pure dephasing. Finally, through proper choice of magnetic field orientation, the electric-dipole spin resonance via the synthetic SOC can be improved with potential applications in spin-based quantum computing.

Effects of optical lattices on bright solitons in spin-orbit coupled Bose-Einstein condensates

The stationary bright solitons that appear in the ground state of the spin-orbit coupled Bose-Einstein condensate (SOC-BEC) exhibit nodes. We consider SOC-BEC in combined linear and nonlinear optical lattices and study their effects on the matter-wave bright soliton and find that the parameters of the nonlinear lattice or atomic scattering length can be judiciously manipulated to have useful control over the nodes of the soliton. It is seen that the soliton with large number of nodes is less stable compared to one having fewer number of nodes. We infer that the synthetic spin-orbit coupling induces instability in the ordinary matter-wave soliton.

Controlling Synthetic Spin-Orbit Coupling in a Silicon Quantum Dot with Magnetic Field

Tunable synthetic spin-orbit coupling (s-SOC) is one of the key challenges in various quantum systems, such as ultracold atomic gases, topological superconductors, and semiconductor quantum dots. Here we experimentally demonstrate controlling the s-SOC by investigating the anisotropy of spin-valley resonance in a silicon quantum dot. As we rotate the applied magnetic field in-plane, we find a striking nonsinusoidal behavior of resonance amplitude that distinguishes s-SOC from the intrinsic spin-orbit coupling (i-SOC), and associate this behavior with the previously overlooked in-plane transverse magnetic field gradient. Moreover, by theoretically analyzing the experimentally measured s-SOC field, we predict the quality factor of the spin qubit could be optimized if the orientation of the in-plane magnetic field is rotated away from the traditional working point.

Stripe and junction-vortex phases in linearly coupled Bose-Einstein condensates

Soon after its theoretical prediction, striped-density states in the presence of synthetic spin-orbit coupling were realized in Bose-Einstein condensates of ultracold neutral atoms [J.-R. Li et al., Nature 543, 91 (2017)]. The achievement opens avenues to explore the interplay of superfluidity and crystalline order in the search for supersolid features and materials. The system considered is essentially made of two linearly coupled Bose-Einstein condensates, that is, a pseudo-spin-$1/2$ system, subject to a spin-dependent gauge field ${\ensuremath{\sigma}}_{z}\ensuremath{\hbar}{k}_{\ensuremath{\ell}}$. Under these conditions, the stripe phase is achieved when the linear coupling $\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}/2$ is small against the gauge energy $m\mathrm{\ensuremath{\Omega}}/\ensuremath{\hbar}{k}_{\ensuremath{\ell}}^{2}<1$. The resulting density stripes have been interpreted as a standing-wave interference pattern with approximate wave number $2{k}_{\ensuremath{\ell}}$. Here, we show that the emergence of the stripe phase is induced by an array of Josephson vortices living in the junction defined by the linear coupling. As happens in superconducting junctions subject to external magnetic fields, a vortex array is the natural response of the superfluid system to the presence of a gauge field. Also similar to superconductors, the Josephson currents and their associated vortices can be present as a metastable state in the absence of gauge field. We provide closed-form solutions to the 1D mean-field equations that account for such vortex arrays. The underlying Josephson currents coincide with the analytical solutions to the sine-Gordon equation for the relative phase of superconducting junctions [C. Owen and D. Scalapino, Phys. Rev. 164, 538 (1967)].

Bose–Einstein condensates under a non-Hermitian spin–orbit coupling* *Project supported by the National Natural Science Foundation of China (Grant No. 11974331).

We study the properties of Bose–Einstein condensates under a non-Hermitian spin–orbit coupling (SOC), induced by a dissipative two-photon Raman process. We focus on the dynamics of the condensate at short times, when the impact of decoherence induced by quantum jumps is negligible and the dynamics is coherently driven by a non-Hermitian Hamiltonian. Given the significantly modified single-particle physics by dissipative SOC, the interplay of non-Hermiticity and interaction leads to a quasi-steady-state phase diagram different from its Hermitian counterpart. In particular, we find that dissipation can induce a phase transition from the stripe phase to the plane-wave phase. We further map out the phase diagram with respect to the dissipation and interaction strengths, and finally investigate the stability of quasi-steady states through the time-dependent dissipative Gross–Pitaevskii equation. Our results are readily accessible based on standard experiments with synthetic spin–orbit couplings.

Dissipation-facilitated molecules in a Fermi gas with non-Hermitian spin-orbit coupling

We study the impact of non-Hermiticity on the molecule formation in a two-component spin-orbit-coupled Fermi gas near a wide Feshbach resonance. Under an experimentally feasible configuration where the two-photon Raman process is dissipative, the Raman-induced synthetic spin-orbit coupling acquires a complex strength. Remarkably, dissipation of the system facilitates the formation and binding of molecules, which, despite their dissipative nature and finite lifetime, exist over a wider parameter regime than in the corresponding Hermitian system. These dissipation-facilitated molecules can be probed by the inverse radio-frequency (rf) spectroscopy, provided the Raman lasers are blue detuned to the excited state. The effects of dissipation manifest in the rf spectra as shifted peaks with broadened widths, which serve as a clear experimental signature. Our results, readily observable in current cold-atom experiments, shed light on the fascinating interplay of non-Hermiticity and interaction in few- and many-body open quantum systems.

Commensurate-incommensurate supersolid ground state of a spin-orbit-coupled Bose-Einstein condensate in one-dimensional optical lattices

Supersolid, a fascinating quantum state of matter, features novel phenomena such as the non-classical rotational inertia and transport anomalies. It is a long standing issue of the coexistence of superfluidity and broken translational symmetry in condensed matter physics. By recent experimental advances to create tunable synthetic spin-orbit coupling in ultracold gases, such highly controllable atomic systems would provide new possibilities to access supersolidity with no counterpart in solids. Here we report that the combination of anharmonicity of trapping potential and spin-orbit coupling will provide a new paradigm to achieve supersolids. By means of imaginary time evolution of the Gross-Pitaevskii equation, we demonstrate that a supersolid state can be found when considering a trapped Rashba-type spin-orbit coupled bosonic atoms loaded in a one-dimensional optical lattice. Furthermore, a skyrmion-anti-skyrmion lattice is associated with the appearance of such supersoildity, indicating the topological nontrivial properties of our proposed supersolids.

Tools for quantum simulation with ultracold atoms in optical lattices

After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity where it can be used to investigate complex quantum processes. Planning of new experiments and upgrading existing set-ups depends crucially on a broad overview of the available techniques, their specific advantages and limitations. This Technical Review aims to provide a comprehensive compendium of the state of the art. We discuss the basic principles, the available techniques and their current range of applications. Focusing on the simulation of varied phenomena in solid-state physics using optical lattice experiments, we review their basics, the necessary techniques and the accessible physical parameters. We outline how to control and use interactions with external potentials and between the atoms, and how to design new synthetic gauge fields and spin-orbit coupling. We discuss the latest progress in site-resolved techniques using quantum gas microscopes, and describe the unique features of quantum simulation experiments with two-electron atomic species.

Acoustic spin-Chern insulator induced by synthetic spin\u2013orbit coupling with spin conservation breaking

Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. However, both the route of implementing an analogue of the quantum Hall effect as well as the quantum spin Hall effect are obstructed for acoustics by the requirement of a magnetic field, or the presence of fermionic quantum statistics, respectively. Here, we construct a two-dimensional topological acoustic crystal induced by the synthetic spin-orbit coupling, a crucial ingredient of topological insulators, with spin non-conservation. Our setup allows us to free ourselves of symmetry constraints as we rely on the concept of a non-vanishing “spin” Chern number. We experimentally characterize the emerging boundary states which we show to be gapless and helical. More importantly, we observe the spin flipping transport in an H-shaped device, demonstrating evidently the spin non-conservation of the boundary states.

Synthetic spin-orbit coupling mediated by a bosonic environment

We study a mobile quantum impurity, possessing internal rotational degrees of freedom, confined to a ring in the presence of a many-particle bosonic bath. By considering the recently introduced rotating polaron problem, we define the Hamiltonian and examine the energy spectrum. The weak-coupling regime is studied by means of a variational ansatz in the truncated Fock space. The corresponding spectrum indicates that there emerges a coupling between the internal and orbital angular momenta of the impurity as a consequence of the phonon exchange. We interpret the coupling as a phonon-mediated spin-orbit coupling and quantify it by using a correlation function between the internal and orbital angular momentum operators. The strong-coupling regime is investigated within the Pekar approach and it is shown that the correlation function of the ground state shows a kink at a critical coupling, that is explained by a sharp transition from the non-interacting state to the states that exhibit strong interaction with the surroundings. The results might find applications in such fields as spintronics or topological insulators, where spin-orbit coupling is of crucial importance.

Strongly interacting spin-orbit coupled Bose-Einstein condensates in one dimension

We theoretically study dilute superfluidity of spin-1 bosons with antiferromagnetic interactions and synthetic spin-orbit coupling (SOC) in a one-dimensional lattice. Employing a combination of density matrix renormalization group and quantum field theoretical techniques we demonstrate the appearance of a robust superfluid spin-liquid phase in which the spin-sector of this spinor Bose-Einstein condensate remains quantum disordered even after introducing quadratic Zeeman and helical magnetic fields. Despite remaining disordered, the presence of these symmetry breaking fields lifts the perfect spin-charge separation and thus the nematic correlators obey power-law behavior. We demonstrate that, at strong coupling, the SOC induces a charge density wave state that is not accessible in the presence of linear and quadratic Zeeman fields alone. In addition, the SOC induces oscillations in the spin and nematic expectation values as well as the bosonic Green's function. These non-trivial effects of a SOC are suppressed under the application of a large quadratic Zeeman field. We discuss how our results could be observed in experiments on ultracold gases of $^{23}$Na in an optical lattice.

Some recent progresses on the study of ultracold quantum gases with spin-orbit coupling

Artificial synthetic gauge field and spin-orbit coupling has been extensively studied following their experimental realization in ultracold atomic systems. Thanks for the versatile controllability, such systems not only provide possibilities to simulate and study important models in multidisciplinary fields of physics, but also work as an excellent platform to engineer novel states of matter and quantum phenomena. This paper reviews some recent progresses on the study of ultracold atomic systems with spin-orbit coupling, focusing on the effects induced by dissipation, novel interaction forms, large symmetry of spins, and long-range interactions. The investigation in these aspects is closely related to the characteristics of ultracold atomic systems, hence can bring new inspirations and perspectives on the understanding of spin-orbit coupling. In this review, we firstly investigate the appearance of a topological superradiant state in a quasi-one-dimensional Fermi gas with cavity-assisted Raman process. A cavity-assisted spin-orbit coupling and a bulk gap opening at half filling will be induced by the superradiant light generated in the transversely driven cavity mode. The topological superradiant state and the corresponding topological phase transition in the system can be driven by this mechanism. Then, symmetry-protected topological states of interacting fermions will be introduced in a quasi-one-dimensional cold gas of alkaline-earth-like atoms. Raman-assisted spin-orbit couplings in the clock states, together with the spin-exchange interactions in the clock-state manifolds will give rise to symmetry-protected topological states for interacting fermions, by taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these alkaline-earth-like atoms. Furthermore, we show that an exotic topological defect, double-quantum spin vortices, which are characterized by doubly quantized circulating spin currents and unmagnetized filled cores, can exist in the ground states of SU(3) spin-orbit-coupled Bose-Einstein condensates. It is found that the combined effects of SU(3) spin-orbit coupling and spin-exchange interaction determine the ground-state phase diagram. Finally, we demonstrate that spin-orbit coupling and soft-core long-range interaction can induce an exotic supersolid phase of Bose gas, with the emergence of spontaneous circulating particle current. This implies that a finite angular momentum can be generated with neither external rotation nor synthetic magnetic field, and the direction of the angular momentum can be altered by adjusting the strength of spin-orbit coupling or interatomic interaction.