In this paper, we present an experimental approach for simulating and detecting topological invariants using ultracold fermions confined in two-dimensional hexagonal optical lattices. We propose achieving degenerate four-band models with nontrivial topologies in both the AII and A classes by introducing additional inertial forces, Raman processes, or periodic driving. By implementing various quench sequences and observing the evolution of the time-of-flight pattern, we can gather comprehensive information about the ground states and determine the topological property of the valence bands. Through the analysis of tomographic results, we are able to extract and calculate the spin Chern number. Additionally, we demonstrate the robustness of the quantized topological invariants and discuss the effects of various experimental parameters.

In a trapped-ion system, accurate thermometry of ions is crucial for precisely evaluating the system state and performing quantum operations. However, when the motional state of a single ion is far away from the ground state, the spatial dimensionality of the phonon state sharply increases. Then it is difficult to realize accurate and mode-resolved thermometry with existing methods. In this work, we apply deep learning to the thermometry of a trapped ion and propose an efficient and mode-resolved method for accurately estimating large mean phonon numbers. We have also conducted experimental verification based on a self-developed surface trap. The result has shown the significant accuracy and efficiency of the method for thermometry of a single ion with large mean phonon numbers. The mode-resolved feature of our method makes it better applied to the characterization of system parameters, such as evaluating cooling effectiveness and analyzing surface trap noise. Our trained neural network model can be easily extended to other experimental setups and parameter ranges without modification of the experimental setups.

The quantum switch, the canonical example of a process with indefinite causal order, has been claimed to provide various advantages over processes with definite causal orders for some particular tasks in the field of quantum metrology. In this work, we argue that some of these advantages in fact do not hold if a fairer comparison is made. To this end, we consider a framework that allows for a proper comparison between the performance, quantified by the quantum Fisher information, of different classes of indefinite causal order processes and that of causal strategies on a given metrological task. More generally, by considering the recently proposed classes of circuits with classical or quantum control of the causal order, we come up with different examples where processes with indefinite causal order offer (or not) an advantage over processes with definite causal order, qualifying the interest of indefinite causal order regarding quantum metrology. As it turns out, for a range of examples, the class of quantum circuits with quantum control of causal order, which are known to be physically realizable, is shown to provide a strict advantage over causally ordered quantum circuits as well as over the class of quantum circuits with causal superposition. Thus, the consideration of this class provides new evidence that indefinite causal order strategies can strictly outperform definite causal order strategies in quantum metrology.

The monochromatic driving of a quantum system is a successful technique in quantum simulations, well captured by an effective Hamiltonian approach, and with applications in artificial gauge fields and topological engineering. Here, we investigate multichromatic Floquet driving for quantum simulation. Within a well-defined range of parameters, we show that the time coarse-grained dynamics of such a driven closed quantum system is encapsulated in an effective master equation for the time-averaged density matrix, that evolves under the action of an effective Hamiltonian and tunable Lindblad-type dissipation or quantum gain terms. As an application, we emulate the dissipation induced by phase noise and incoherent emission or absorption processes in the bichromatic driving of a two-level system, and reproduce the phase decoherence in a harmonic oscillator model.

The coherent quantum transport of matter wave through a ring-shaped circuit attached to leads defines an iconic system in mesoscopic physics that has allowed researchers to both explore fundamental questions in quantum science and to draw important avenues for conceiving devices of practical use. Here we study the source-to-drain transport of excitations going through a ring network, without propagation of matter waves. We model the circuit in terms of a spin system with specific long-range interactions that are relevant for quantum technology, such as Rydberg atoms trapped in optical tweezers or ion traps. Inspired by the logic of rf- and dc-SQUIDs, we consider rings with one and two local energy offsets, or detunings. As a combination of specific phase shifts in going through the localized detunings and as a result of coherent tunneling, we demonstrate how the transport of excitations can be controlled, with a distinctive dependence on the range of interactions.

The non-Hermitian skin effect (NHSE), characterized by the collapse of bulk-band eigenstates into the localized boundary modes of the systems, is one of most striking properties in the field of non-Hermitian physics. Unique physical phenomena related to the NHSE have attracted a great deal of interest; however, their experimental realization usually requires nonreciprocal hopping, which faces a great challenge in ultracold-atom systems. In this work we propose the realization of the NHSE in a one-dimensional optical lattice by periodically driven ultracold atoms in the presence of staggered atomic loss. By studying the effective Floquet Hamiltonian in the high-frequency approximation, we reveal the underlying mechanism for the periodic-driving-induced NHSE. We find that the robust NHSE can be tuned by the driving phase, which is manifested by the dynamical localization. Most remarkably, we uncover the periodic-driving-induced critical skin effect for two coupled chains with different driving phases, accompanied by the appearance of size-dependent topological in-gap modes. Our study provides a feasible way to observe the NHSE and explore the corresponding unique physical phenomena due to the interplay of non-Hermiticity and many-body statistics in ultracold-atom systems.

In a parallel publication [Phys. Rev. Lett. 132, 263401 (2024)] we demonstrate that photoinduced two-body loss can be used to measure Tan's contact with high precision in a two-component Fermi gas. Here, in the present companion paper, we provide relevant background information on this work and describe in detail the methodology for both the experiments and the data analysis. We first review various theoretical approaches for calculating the contact and identify areas in phase space of the spin-balanced Fermi gas where Tan's contact has not yet been determined. Next, we provide detailed information on our experimental methods, in particular, explaining the measurement and calibration procedures to achieve a high-precision results for the contact. Afterwards, we study the variation of the decay laws of two-body loss in a Fermi gas in the crossover from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein-condensate (BEC) regime, verifying previous predictions. Finally, we determine the closed-channel fraction of the Fermi gas and compare it to previous measurements and theoretical calculations.

We consider a ring-shaped triple-well potential with few polar bosons with in-plane dipole orientation. By diagonalizing the extended Bose-Hubbard Hamiltonian, we investigate the ground-state properties of the system as we rotate the dipole angle and vary the on-site and dipole-dipole interaction strengths. We find that the anisotropic character of the dipolar interactions, as well as the competition between dipole and on-site interactions, leads to different ground states and that the entanglement between sites also depends on the number of particles. We further characterize the system by studying the condensed fraction and coherence properties for different polarization angles, highlighting the possible effect of the dipolar interaction as a manipulation tool.

Periodical corrugation in the dielectric slab transforms the two waveguide modes at zero Bloch wave number into a leaky resonant mode and symmetry-protected bound states in the continuum (BIC) with a small frequency detuning. The leaky resonant mode can be directly excited by a weakly linearly polarized normally incident optical field. In the presence of Kerr nonlinearity, BIC can be indirectly excited by an optically bistable response. Two types of bistable operations were considered. For the first type, the intensity of the incident field was gradually increased to exceed the critical value and then decreased to zero. For the second type, the intensity was fixed, while the linear polarization angle of the incident field was gradually increased to exceed a critical value and then decreased to $0^{\circ }$. Theoretically, the indirectly excited BIC can store optical energy without loss, even when the intensity of the incident field decreases to zero. The incidence of an optical field with double frequency or orthogonal linear polarization can erase the stored optical field by destroying BIC. The proposed system can function as an optical storage and switching device.

Two interacting Rydberg atoms coupled to a waveguide may realize a giant-atom platform that exhibits controllable (phase-dependent) chirality through which the direction of nonreciprocally scattered photons can be switched on demand, e.g., by the geometrical tuning of an external driving field. In our platform, at variance with traditional setups, the chirality arises from a simple optical implementation of the local phase difference between two coupling points of the Rydberg giant atom. When employing two (or more) driving fields, this platform can also be used as a frequency converter with its strongly asymmetric efficiency being significantly enhanced via the chiral couplings. Our Rydberg giant-atom platform is well suited for chiral quantum optics applications and further offers direct scalability for reaching tunable frequency conversion in the optical domain.

We present a theory for quantum nondemolition (QND) measurements of an atomic ensemble in the presence of spontaneous emission. We derive the master equation that governs the evolution of the ground state of the atoms and the quantum state of light. Solving the master equation exactly without invoking the Holstein-Primakoff approximation and projecting out the quantum state of light, we derive a positive operator-valued measure that describes the QND measurement. We show that, at high spontaneous emission conditions, the QND measurement has a unique dominant state to which the measurement collapses. We additionally investigate the behavior of the QND measurement in the limiting case of strong atom-light interactions, where we show that the positive operator valued measure becomes a projection operator. We further analyze the effect of spontaneous emission noise on atomic state preparation. We find that it limits the width of the eigenvalue spectrum available to a quantum state in a linear superposition. This effect leads to state collapse on the dominant state. We generate various nonclassical states of the atom by tuning the atom-light interaction strength. We find that nonclassical states such as the Schrödinger-cat state, whose coherence spans the entire eigenvalue spectrum of the total spin operator $J_z$ for a given spin eigenvalue $J$, lose their coherence because spontaneous emission limits the accessibility of states farther away from the dominant state.

Master equations play a pivotal role in investigating open quantum systems. In particular, the Bloch-Redfield equation stands out due to its relation to a concrete physical environment. However, without further approximations it does not lead to a Lindblad master equation that guarantees that the density matrix stays completely positive, which has raised some concerns regarding its use. This study builds on previous efforts to transform the Bloch-Redfield framework into a mathematically robust Lindblad equation while fully preserving the effects that are lost within the secular approximation that is commonly used to guarantee positivity. These previous approaches introduced two potential deficiencies: The environment-induced energy shift can be non-Hermitian and some decay rates can be negative, violating the assumptions of Lindblad's theorem. Here we propose and evaluate straightforward solutions to both problems. Our approach offers an effective and general procedure for obtaining a Lindblad equation, derived from a concrete physical environment, while mitigating the unphysical dynamics present in the Bloch-Redfield equation.

Microwave single-photon detection is one of the critical tasks for the implementation of the desired microwave quantum information processing. Given the detection efficiency of the demonstrated microwave single-photon detector is still very limited, here, we propose a nonreciprocity detector array to implement high-efficiency detection of a single itinerant microwave photon, transported along a one-dimensional waveguide. We show that different from the reciprocity array with more than 20 atomic detectors [Romero et al., Phys. Rev. Lett. 102, 173602 (2009)] for ideal detection, the nonreciprocity array with just three atomic detectors is sufficient to achieve deterministic detection (i.e., the achievable probability approaches $100\%$) of a single itinerant microwave photon. Specifically, we design an array with a few current-biased Josephson junctions individually coupled to a common microwave transmission line and then discuss its feasibility.

Hamiltonian simulation is a major application of quantum computing, for example, enabling prediction of the properties of molecules. Prior work has used product formulas with randomization to improve performance, but has only yielded modest improvements over the excellent performance provided by deterministic high-order product formulas. In this work, we provide a randomized scheme that greatly increases the order of product formulas, thereby providing a large advantage over the best-performing deterministic schemes. Our scheme is based on applying randomly chosen corrections to a high-order symmetric product formula. If the original product formula is of order $2k$ (so the error is of order $2k+1$), then the corrected formula is of order $4k+1$, corresponding to a doubling of the order of the error. In practice, applying the corrections in a quantum algorithm requires some structure to the Hamiltonian, for example, the Pauli strings as are commonly used in the simulation of quantum chemistry.

Quantum batteries (QBs) are energy storage and transfer microdevices that open up new possibilities in energy technology. Here, we derive a resonator–multiple-qutrit quantum battery (QB) model consisting of a multimode resonator and $N$ superconducting transmon qutrits. We investigate the charging and self-discharging performances of the QBs and discuss the roles of quantum coherence and quantum entanglement. The results show that environment noise is not always detrimental for QB systems. The QB with efficient charging, stable energy-storage, and slow self-discharging processes can be realized by considering the dephasing noise and manipulating the energy gap. We find that the charging energy is positively related to coherence and entanglement while the stable energy and the self-discharging energy are negatively related to coherence. The phenomenon of the vanishing entanglement corresponds to the dynamic decoupling behavior of the QB's steady states. Our results provide a way to realize many-body QBs on a superconducting circuit platform.

Nonadiabatic holonomic quantum computation has been proposed as a method to implement quantum logic gates with robustness comparable to that of adiabatic holonomic gates but with shorter execution times. In this paper, we establish an isoholonomic inequality for quantum gates, which provides a lower bound on the lengths of cyclic transformations of the computational space that generate a specific gate. Then, as a corollary, we derive a nonadiabatic execution time estimate for holonomic gates. In addition, we demonstrate that under certain dimensional conditions, the isoholonomic inequality is tight in the sense that every gate on the computational space can be implemented holonomically and unitarily in a time-optimal way. We illustrate the results by showing that the procedures for implementing a universal set of holonomic gates proposed in a pioneering paper on nonadiabatic holonomic quantum computation saturate the isoholonomic inequality and are thus time optimal.

Probabilistic error cancellation (PEC) is a technique that generates error-mitigated estimates of expectation values from ensembles of quantum circuits. In this work we extend the application of PEC from unitary-only circuits to dynamic circuits with midcircuit measurements and classically controlled (feedforward) Clifford operations. Our approach extends the sparse Pauli-Lindblad noise model from characterizing gates to characterizing target channels containing midcircuit measurements and feedforward while accounting for nonlocal measurement crosstalk in superconducting processors. Our mitigation and monitoring experiments provide a holistic view for the performance of the protocols developed in this work. These capabilities will be a crucial tool in the exploration of near-term dynamic circuit applications.

In this paper we present a unified treatment of three-body atoms and molecules using numerical tensor methods. The Schrödinger equation in perimetric coordinates is recast in a canonical tensor format. It is shown that the Schrödinger equation can be solved in this full-tensor format but that by using a low-rank tensor decomposition, in particular the tensor-train and quantized-tensor-train formats, energies accurate to at least the nanohartree can be obtained for the He atom (in which the mass of the uniquely charged particle is much greater than the other two particles), the positronium negative ion (${\mathrm{Ps}}^{-}$, in which all the masses are equal), and the non-Born-Oppenheimer ${\mathrm{H}}_2{}^{+}$ molecule (in which the mass of the uniquely charged particle is much smaller than the other two particles).