Counter-diabatic driving (CD) is a technique in quantum control theory designed to counteract nonadiabatic excitations and guide the system to follow its instantaneous energy eigenstates, and hence has applications in state preparation, quantum annea
ling, and quantum thermodynamics. However, in many practical situations, the effect of the environment cannot be neglected, and the performance of the CD is expected to degrade. To arrive at universal bounds on the resulting error of CD in this situation we consider a driven spin-boson model as a prototypical setup. The inequalities we obtain, in terms of either the Bures angle or the fidelity, allow us to estimate the maximum error solely characterized by the parameters of the system and the bath. By utilizing the analytical form of the upper bound, we demonstrate that the error can be systematically reduced through optimization of the external driving protocol of the system. We also show that if we allow a time-dependent system-bath coupling angle, the obtained bound can be saturated and realizes unit fidelity.
We develop two cutting-edge approaches to construct deep neural networks representing the purified finite-temperature states of quantum many-body systems. Both methods commonly aim to represent the Gibbs state by a highly expressive neural-network wa
ve function, exemplifying the idea of purification. The first method is an entirely deterministic approach to generate deep Boltzmann machines representing the purified Gibbs state exactly. This strongly assures the remarkable flexibility of the ansatz which can fully exploit the quantum-to-classical mapping. The second method employs stochastic sampling to optimize the network parameters such that the imaginary time evolution is well approximated within the expressibility of neural networks. Numerical demonstrations for transverse-field Ising models and Heisenberg models show that our methods are powerful enough to investigate the finite-temperature properties of strongly correlated quantum many-body systems, even when the problematic effect of frustration is present.
Topological matter and topological optics have been studied in many systems, with promising applications in materials science and photonics technology. These advances motivate the study of the interaction between topological matter and light, as well
as topological protection in light-matter interactions. In this work, we study a waveguide-interfaced topological atom array. The light-matter interaction is nontrivially modified by topology, yielding novel optical phenomena. We find topology-enhanced photon absorption from the waveguide for large Purcell factor, i.e., $Gamma/Gamma_0gg 1$, where $Gamma$ and $Gamma_0$ are the atomic decays to waveguide and environment, respectively. To understand this unconventional photon absorption, we propose a multi-channel scattering approach and study the interaction spectra for edge- and bulk-state channels. We find that, by breaking inversion and time-reversal symmetries, optical anisotropy is enabled for reflection process, but the transmission is isotropic. Through a perturbation analysis of the edge-state channel, we show that the anisotropy in the reflection process originates from the waveguide-mediated non-Hermitian interaction. However, the inversion symmetry in the non-Hermitian interaction makes the transmission isotropic. At a topology-protected atomic spacing, the subradiant edge state exhibits huge anisotropy. Due to the interplay between edge- and bulk-state channels, a large topological bandgap enhances nonreciprocal reflection of photons in the waveguide for weakly broken time-reversal symmetry, i.e., $Gamma_0/Gammall 1$, producing complete photon absorption. We show that our proposal can be implemented in superconducting quantum circuits. The topology-enhanced photon absorption is useful for quantum detection. This work shows the potential to manipulate light with topological quantum matter.
We consider complex 3D polarizations in the interference of several vector wave fields with different commensurable frequencies and polarizations. We show that the resulting polarizations can form knots, and interfering three waves is sufficient to g
enerate a variety of Lissajous, torus, and other knot types. We describe the spin angular momentum, generalized Stokes parameters and degree of polarization for such knotted polarizations, which can be regarded as partially-polarized. Our results are generic for any vector wave fields, including, e.g., optical and acoustic waves. As a directly-observable example, we consider knotted trajectories of water particles in the interference of surface water (gravity) waves with three different frequencies.
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. The latter emerge in the unraveling of Markovian quantum master equations and/or in continuous quantum measurements. Ensemble-averaging quantum trajector
ies at the occurrence of quantum jumps, i.e., the jumptimes, gives rise to a discrete, deterministic evolution which is highly sensitive to the presence of dark states. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians, which is also reflected by the corresponding jumptime dynamics. The topological character of the latter can then be observed, for instance, in the transport behavior, exposing an infinite hierarchy of topological phase transitions. We develop our theory for one- and two-dimensional two-band Hamiltonians, and show that the topological behavior is directly manifest for chiral, PT, or time reversal-symmetric Hamiltonians.
We analyze planar electromagnetic waves confined by a slab waveguide formed by two perfect electrical conductors. Remarkably, 2D Maxwell equations describing transverse electromagnetic modes in such waveguides are exactly mapped onto equations for ac
oustic waves in fluids or gases. We show that interfaces between two slab waveguides with opposite-sign permeabilities support 1D edge modes, analogous to surface acoustic plasmons at interfaces with opposite-sign mass densities. We analyze this novel type of edge modes for the cases of isotropic media and anisotropic media with tensor permeabilities (including hyperbolic media). We also take into account `non-Hermitian edge modes with imaginary frequencies or/and propagation constants. Our theoretical predictions are feasible for optical and microwave experiments involving 2D metamaterials.
Adiabatic pumping is characterized by a geometric contribution to the pumped charge, which can be non-zero even in the absence of a bias. However, as the driving speed is increased, non-adiabatic excitations gradually reduce the pumped charge, thereb
y limiting the maximal applicable driving frequencies. To circumvent this problem, we here extend the concept of shortcuts to adiabaticity to construct a control protocol which enables geometric pumping well beyond the adiabatic regime. Our protocol allows for an increase, by more than an order of magnitude, in the driving frequencies, and the method is also robust against moderate fluctuations of the control field. We provide a geometric interpretation of the control protocol and analyze the thermodynamic cost of implementing it. Our findings can be realized using current technology and potentially enable fast pumping of charge or heat in quantum dots, as well as in other stochastic systems from physics, chemistry, and biology.
We introduce jumptime unraveling as a distinct method to analyze quantum jump trajectories and the associated open/continuously monitored quantum systems. In contrast to the standard unraveling of quantum master equations, where the stochastically ev
olving quantum trajectories are ensemble-averaged at specific times, we average quantum trajectories at specific jump counts. The resulting quantum state then follows a discrete, deterministic evolution equation, with time replaced by the jump count. We show that, for systems with finite-dimensional state space, this evolution equation represents a trace-preserving quantum dynamical map if and only if the underlying quantum master equation does not exhibit dark states. In the presence of dark states, on the other hand, the state may decay and/or the jumptime evolution eventually terminate entirely. We elaborate the operational protocol to observe jumptime-averaged quantum states, and we illustrate the jumptime evolution with the examples of a two-level system undergoing amplitude damping or dephasing, a damped harmonic oscillator, and a free particle exposed to collisional decoherence.
We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular mom
entum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a ${it scalar}$ potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement ${it vector}$ potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential representations, we put forward an acoustic ${it spinor}$ representation combining the scalar and vector representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.
We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states or simple mixed states, which exhibit
dominant eigenstates and thus lend themselves to low-rank approximations. The developed scheme is applicable to any pure-state tomography method, promoting it to mixed-state tomography. Here, we demonstrate it with machine learning-inspired pure-state tomography based on neural-network representations of quantum states. The latter have been shown to efficiently approximate generic classes of complex (pure) states of large quantum systems. We test our method by applying it to experimental data from trapped ion experiments with four to eight qubits.
