Observation of the ground-state geometric phase in a Heisenberg XY model

Phase and Amplitude Modes in the Anisotropic Dicke Model with Matter Interactions

Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein-Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms.

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Observation of geometric phase effect through backward angular oscillations in the H + HD → H2 + D reaction

Quantum interference between reaction pathways around a conical intersection (CI) is an ultrasensitive probe of detailed chemical reaction dynamics. Yet, for the hydrogen exchange reaction, the difference between contributions of the two reaction pathways increases substantially as the energy decreases, making the experimental observation of interference features at low energy exceedingly challenging. We report in this paper a combined experimental and theoretical study on the H + HD → H2 + D reaction at the collision energy of 1.72 eV. Although the roaming insertion pathway constitutes only a small fraction (0.088%) of the overall contribution, angular oscillatory patterns arising from the interference of reaction pathways were clearly observed in the backward scattering direction, providing direct evidence of the geometric phase effect at an energy of 0.81 eV below the CI. Furthermore, theoretical analysis reveals that the backward interference patterns are mainly contributed by two distinct groups of partial waves (J ~ 10 and J ~ 19). The well-separated partial waves and the geometric phase collectively influence the quantum reaction dynamics.

Theory and calculation of abelian and non-abelian geometric phase factors with SpinDynamica

Cyclic quantum evolution is accompanied by a systematic change in the phase of the initial state vector. This change only depends upon the path traced out by the system itself. Such effects are collectively known as geometric phase factors. The geometric foundations of these phase factors are most elegantly formulated in terms of fibre bundle theory and differential forms, both of which can represent a significant hurdle to master. We present a derivation of the abelian and non-abelian Berry phase in terms of embedded manifolds of linear vector spaces. Embedded manifolds offer the advantage of being less abstract than fibre bundles, and are well-suited for explicit calculations. Essential features of the derivation reduce to matrix-vector manipulations. We further discuss a numerical strategy for the calculation of abelian and non-abelian phase factors. Our approach is based upon Hungarian method and the polar decomposition, and is made freely available as a SpinDynamica addon. Additionally, all derivations and analytic calculations are supported by Mathematica notebooks.

Phase diagram and quantum criticality of a non-HermitianXYmodel with a complex transverse field

We study a one dimensional non-Hermitian quantumXYmodel with a complex transverse field, where the imaginary transverse field can be generated by three-level atoms with spontaneous decay. Many-body spectrum can be obtained analytically. The phase diagram in thermodynamical limit indicates that the imaginary transverse field induces non-Hermitian degeneracy and shrinks the ferromagnetic phase for anisotropic interaction. We also analyze the effect of imaginary field on quantum criticality through ground state geometry phase. It causes a shift of transition point but does not change the order of phase transition in anisotropic interaction region. However, the phase transition is related to the original Hermitian degeneracy in anisotropic interaction region, which indicates that the imaginary transverse field cannot change phase boundary and critical behavior.

Scaling of the Berry Phase in the Yang-Lee Edge Singularity

We study the scaling behavior of the Berry phase in the Yang-Lee edge singularity (YLES) of the non-Hermitian quantum system. A representative model, the one-dimensional quantum Ising model in an imaginary longitudinal field, is selected. For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES. We find that the real and imaginary parts of the complex Berry phase show anomalies around the critical points of YLES. In the overlapping critical regions constituted by the (0 + 1)D YLES and (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT), we find that the real and imaginary parts of the Berry phase can be described by both the (0 + 1)D YLES and (1 + 1)D FPPT scaling theory. Our results demonstrate that the complex Berry phase can be used as a universal order parameter for the description of the critical behavior and the phase transition in the non-Hermitian systems.

Floquet-engineered quantum state transfer in spin chains

Quantum state transfer between two distant parties is at the heart of quantum computation and quantum communication. Among the various protocols, the counterdiabatic driving (CD) method, by suppressing the unwanted transitions with an auxiliary Hamiltonian H_cd(t), offers a fast and robust strategy to transfer quantum states. However, H_cd(t) term often takes a complicated form in higher-dimensional systems and is difficult to realize in experiment. Recently, the Floquet-engineered method was proposed to emulate the dynamics induced by H_cd(t) without the need for complex interactions in multi-qubit systems, which can accelerate the adiabatic process through the fast-oscillating control in the original Hamiltonian H₀(t). Here, we apply this method in the Heisenberg spin chains, with only control of the two marginal couplings, to achieve the fast, high-fidelity, and robust quantum state transfer. Then we report an experimental implementation of our scheme using a nuclear magnetic resonance simulator. The experimental results demonstrate the feasibility of this method in complex many-body system and thus provide a new alternative to realize the high-fidelity quantum state manipulation in practice.

Uhlmann curvature in dissipative phase transitions

A novel approach based on the Uhlmann curvature is introduced for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions. NESS-QPTs offer a unique arena where such a distinction fades off. We propose a method to reveal and quantitatively assess the quantum character of such critical phenomena. We apply this tool to a paradigmatic class of lattice fermion systems with local reservoirs, characterised by Gaussian non-equilibrium steady states. The relations between the behaviour of the Uhlmann curvature, the divergence of the correlation length, the character of the criticality and the dissipative gap are demonstrated. We argue that this tool can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations.

Scaling of geometric phase versus band structure in cluster-Ising models

We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by an Ising exchange interaction and external magnetic field. The various phases are studied through winding numbers. They may be ordinary phases with local order parameters or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z=1 or z=2 are found. In particular, the criticality is analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. With this study, we quantify the scaling behavior of the geometric phase in relation to the topology and low-energy properties of the band structure of the system.

Solving quantum ground-state problems with nuclear magnetic resonance

Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10⁻⁵ decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers