Correlations between a system and its environment lead to errors in an open quantum system. Detecting those correlations would be valuable for avoiding and/or correcting those errors. Here we show that we can detect correlations by measuring only the system itself if we know the cause of the interaction between the two, for example, in the case of a dipole-dipole interaction. We investigate the unitary $U$ which is associated with the exchange Hamiltonian and examine the ability to detect initial correlations between a system and its environment for various types of initial states. The states we select are motivated by realistic experimental conditions, and we provide bounds for when we can state with certainty that there are initial system-environment correlations given experimental data.

Quantum sensors offer the capability to reach unprecedented precision by operating at the standard quantum limit (SQL) or beyond by using quantum entanglement. But an emerging class of quantum sensors that use Rydberg electromagnetically induced transparency (EIT) to detect rf electric fields have yet to reach the SQL. In this work we prove that this discrepancy is due to fundamental limitations in the EIT probing mechanism. We derive the optimum sensitivity of a three-level quantum sensor based on EIT, or more generally coherent spectroscopy, and compare this to the SQL. We apply a minimal set of assumptions, while allowing strong probing fields, thermal broadening, and large optical depth. We derive the optimal laser intensities and optical depth, providing specific guidelines for sensitive operation under common experimental conditions. Clear boundaries of performance are established, revealing that ladder-EIT cannot achieve the SQL due to unavoidable absorption loss. The results may be applied to any EIT-based quantum sensor, but we particularly emphasize our results' importance to the growing field of Rydberg quantum sensing.

We present an implementation of a time-dependent multiconfiguration self-consistent-field method [R. Anzaki, T. Sato, and K. L. Ishikawa, Phys. Chem. Chem. Phys. 19, 22008 (2017)] with the full configuration-interaction expansion for coupled electron-nuclear dynamics in diatomic molecules subject to a strong laser field. In this method, the total wave function is expressed as a superposition of different configurations constructed from time-dependent electronic Slater determinants and time-dependent orthonormal nuclear basis functions. The primitive basis functions of nuclei and electrons are strictly independent of each other without invoking the Born-Oppenheimer approximation. Our implementation treats the electronic motion in its full dimensionality on curvilinear coordinates, while the nuclear wave function is propagated on a one-dimensional stretching coordinate with rotational nuclear motion neglected. We apply the present implementation to high-harmonic generation and dissociative ionization of a hydrogen molecule and discuss the role of electron-nuclear correlation.

We study the photoionization of molecule ${\mathrm{H}}_2^{+}$ in an XUV pulse by numerically solving the time-dependent Schrödinger equation simulation and focus on a zeptosecond birth time delay of a photoelectron from the different cores. We propose a simple and robust method to extract accurately the zeptosecond birth time delay with double-slit interference minima. Based on this extraction method, our results show that the birth time delay is strongly affected by the initial bound-electron wave function due to the deviation of the electron emission position from the central core. Furthermore, an experimental scheme is also proposed to testify this wave-function-dependent zeptosecond birth time delay. Our study sheds more light on the ultrafast molecular photoionization dynamics on the zeptosecond timescale.

Cooling down a trapped ion into its motional ground state is a central step for trapped-ion-based quantum information processing. State-of-the-art cooling schemes often work under a set of optimal cooling conditions derived analytically using a perturbative approach, in which the sideband coupling is assumed to be the weakest of all the relevant transitions. As a result, the cooling rate is severely limited. Here we propose to use a quantum control technique powered with automatic differentiation to speed up the classical cooling schemes. We demonstrate the efficacy of our approach by applying it to find the optimal cooling conditions for classical sideband cooling and electromagnetically induced transparency cooling schemes, which are in general beyond the weak-sideband-coupling regime. Based on those numerically found optimal cooling conditions, we show that faster cooling can be achieved while at the same time a low average phonon occupation can be retained.

A semiclassical theory that describes the generation of a coherent anti-Stokes Raman scattering (CARS) signal is presented that maximizes vibrational coherence in a mode predetermined by the pump, the Stokes, and the probe chirped pulse trains and takes into account the field propagation effects in a cloud of molecules. The buildup of the anti-Stokes signal, which may be used as a molecular signature in the backward CARS signal, is demonstrated numerically. The theory is based on the solution of the coupled Maxwell's and Liouville–von Neumann equations and focuses on the quantum effects induced in the target molecules by the control pulse trains. A deep convolutional neural network technique is implemented to evaluate time-dependent phase characteristics of the control fields. The effect of decoherence induced by spontaneous decay and collisional dephasing is examined.

A direct measurement protocol allows reconstructing specific elements of the density matrix of a quantum state without using quantum state tomography. However, the direct measurement protocols to date are primarily based on weak or strong measurements with an ancillary pointer, which interacts with the investigated system to extract information about the specified elements. Here, we present a direct measurement scheme based on phase-shifting operations which do not need ancillary pointers. In this method, estimates of at most six expectation values of projective observables suffice to determine any specific element of an unknown quantum density matrix. A concrete quantum circuit to implement this direct measurement protocol for multiqubit states is provided, which is composed of just single-qubit gates and two multiqubit controlled-phase gates. This scheme is also extended for the direct measurement of the density matrix of continuous-variable quantum states. Our method can be used in quantum information applications where only partial information about the quantum state needs to be extracted, for example, problems such as entanglement witnessing, fidelity estimation of quantum systems, and quantum coherence estimation.

Einstein-Podolsky-Rosen steering describes a quantum correlation in addition to entanglement and Bell nonlocality. However, conceptually different from entanglement and Bell nonlocality, quantum steering has an asymmetric definition. Motivated by the asymmetric definition of quantum steering, we study the steerability of two interacting qubits, which have asymmetric energy levels, coupled with asymmetric environments. The asymmetric (nonequilibrium) environments are two environments with different temperatures or chemical potentials. The Bloch-Redfield equation is applied to study the dynamics of two qubits and its long-time behavior. In our study, the steady-state steerability is determined by an experimentally friendly steering criteria, which demonstrates steering through the entanglement detection. Our results show that the steady states of two asymmetric qubits have the advantage for one direction of steering, compared to the symmetric setup. We also provide analytical results on the minimal coupling strength between the two qubits in order to be steerable. The asymmetric steerability is collectively determined by the nature of the two qubits and the influence from equilibrium or nonequilibrium environments. Nonequilibrium environments with the cost of nonzero entropy production can enhance the steerability in one direction. We also show the strict hierarchy of entanglement, steering, and Bell nonlocality of the nonequilibrium steady states, which shows a richer structure of steering than entanglement and Bell nonlocality.

We study relativistic effects in photoionization of a hydrogen atom exposed to an intense laser pulse of general ellipticity. The frequency of the laser pulse resides in the ultraviolet region. To this end, the semirelativistic approach introduced in Kjellsson Lindblom et al. [T. Kjellsson Lindblom, M. Førre, E. Lindroth, and S. Selstø, Phys. Rev. Lett. 121, 253202 (2018)] is applied. We present in some detail how this approximation is derived from the Dirac equation for elliptically polarized light within the so-called long-wavelength approximation. The validity of the semirelativistic approach is confirmed by direct comparison with the solution of the Dirac equation. It is found that the total ionization yield depends very weakly on ellipticity in the case of ionization from the isotropic ground state. With the excited initial state $n=2$, $\ell =m_{\ell }=1$; however, pronounced ellipticity dependence is seen—in particular at the stabilization peak. Albeit small, relativistic corrections to the ionization probabilities are found. The correction is found to be largest for linear polarization. While relativistic effects tend to reduce the total ionization probability for most intensities considered, we also report a slight relativistic enhancement at comparatively modest field strengths.

Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an $s$-wave scattering length $a<0$ and a three-body scattering hypervolume $D>0$. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquidlike quantum droplet to a normal gas and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurring later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tricritical point, where the three phases, i.e., quantum droplet, superfluid gas, and normal gas, meet. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.

Dynamical localization is the analog of Anderson localization in momentum space, where the system's energy saturates and the single-particle wave functions are exponentially localized in momentum space. In the presence of interactions, in the context of a periodically kicked Bose gas, it has been argued that dynamical localization persists. Focusing on the Tonks (strongly interacting) regime, we show that the many-body dynamically localized phase is effectively thermal, a clear deviation from the breaking of ergodicity observed in standard many-body localized systems. We relate the effective temperature to the driving parameters, and thus quantitatively describe the loss of coherence at large distances in this phase. Contrary to the noninteracting case, the momentum distribution decays as a power-law at large momenta, characterized by an effectively thermal Tan's contact. This is a rare example where driving and many-body (dynamical) localization lead to an effectively ergodic state.

We develop a general formalism to study laser operation in active microring resonators supporting two counterpropagating modes. Our formalism is based on the coupled-mode equations of motion for the field amplitudes in the two counterpropagating modes and a linearized analysis of the small perturbations around the steady state. We show that the devices including an additional S-shaped waveguide establishing a unidirectional coupling between both modes—the so-called “Taiji” resonators—feature a preferred chirality on the laser emission and can ultimately lead to unidirectional lasing even in the presence of sizable backscattering. The efficiency of this mode selection process is further reinforced by the Kerr nonlinearity of the material. This stable unidirectional laser operation can be seen as an effective breaking of $\mathcal{T}$-reversal symmetry dynamically induced by the breaking of the $\mathcal{P}$ symmetry of the underlying device geometry. This mechanism appears as a promising building block to ensure nonreciprocal behaviors in integrated photonic networks and topological lasers without the need for magnetic elements.

An approach is introduced for the nonparametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface-height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step, the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface-height correlation function without initially assuming any particular form for this function (nonparametric inversion). The input data used to validate this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement is obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this is the case for both dielectric and metallic surfaces, for both $p$- and $s$-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust, and contactless method based on in-plane and co-polarized scattering data for the nonparametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surfaces.

The concept of quantum discord aims at unveiling quantum correlations that go beyond those described by entanglement. Its original formulation [L. Henderson and V. Vedral, J. Phys. A: Math. Gen. 34, 6899 (2001); H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)] is difficult to compute even for the simplest case of two-qubits systems. Alternative formulations have been developed to address this drawback, such as the geometric measure of quantum discord [L. Chang and S. Luo, Phys. Rev. A 87, 062303 (2013)] and the local quantum uncertainty [D. Girolami, T. Tufarelli, and G. Adesso, Phys. Rev. Lett. 110, 240402 (2013)] that can be evaluated in closed form for some quantum systems, such as two-qubit systems. We show here that these two measures of quantum discord are equivalent for $2\times D$ dimensional bipartite quantum systems. By considering the relevant example of N00N states for phase estimation in lossy environments, we also show that both metrics of quantum discord quantify the decrease of quantum Fisher information of the phase estimation protocol. Given their ease of computation in $2\times D$ bipartite systems, the geometric measure of quantum discord and the local quantum uncertainty demonstrate their relevance as computable measures of quantum discord.

Constructing quantum circuits for efficient state preparation are central topics in the field of quantum information and computation. As the number of qubits grows quickly, methods to derive large-scale quantum circuits are strongly desired. In this article, we propose the automatically differentiable quantum circuit (ADQC) approach to efficiently prepare quantum many-qubit states in the form of a matrix product state (MPS). A key ingredient is to introduce latent gates whose decompositions give unitary gates that form a quantum circuit. The circuit is optimized by updating the latent gates using backpropagation to minimize the distance between the evolved and target states. Taking the ground states of one-dimensional spin lattice models and random matrix product states as examples, with the number of qubits where processing the full coefficients is unlikely, ADQC obtains high fidelities with small numbers of layers $N_L\sim O\left(1\right)$. Much higher fidelities are obtained compared with the existing state-preparation approach based on the matrix product disentangler. In addition, ADQC provides an efficient representation of many-qubit states, whose number of parameters can be compressed to about $0.1\%\text{–}1\%$ of that in the MPS. Our work sheds light on the “intelligent construction” of quantum circuits for many-qubit systems by combining them with machine learning methods.

By numerically solving the non-Born-Oppenheimer time-dependent Schrödinger equation of ${\mathrm{H}}_2$ in which the dynamics is confined along the laser polarization direction, we study the electron localization in the single-photon dissociative ionization of ${\mathrm{H}}_2$. The single ionization of ${\mathrm{H}}_2$ produces a free electron and ${\mathrm{H}}_2^{+}$, in whose later propagation the Coulomb field of the freed electron may excite ${\mathrm{H}}_2^{+}$ from the $1s{\sigma }_g$ state to $2p{\sigma }_u$ state. The mixture of these two states with opposite parities results in the asymmetric electron localization on the two nuclei after the dissociation of ${\mathrm{H}}_2^{+}$. The simulation result shows that the bound electron prefers being located on the nucleus, which propagates oppositely to the freed electron. The asymmetry parameter is larger if the freed electron has lower energy. The simulation results agree with experimental measurements in the full energy range. This study indicates that the correlation between ${\mathrm{H}}_2^{+}$ and the freed electron can be important and offers a perspective of controlling electron localization in chemical reactions.

We study the optimization of the performance of arbitrary periodically driven thermal machines. Within the assumption of fast modulation of the driving parameters, we derive the optimal cycle that universally maximizes the extracted power of heat engines, the cooling power of refrigerators, and in general any linear combination of the heat currents. We denote this optimal solution as “generalized Otto cycle” since it shares the basic structure with the standard Otto cycle, but it is characterized by a greater number of fast strokes. We bound this number in terms of the dimension of the Hilbert space of the system used as working fluid. The generality of these results allows for a widespread range of applications, such as reducing the computational complexity for numerical approaches, or obtaining the explicit form of the optimal protocols when the system-baths interactions are characterized by a single thermalization scale. In this case, we compare the thermodynamic performance of a collection of optimally driven noninteracting and interacting qubits. Remarkably, for refrigerators the noninteracting qubits perform almost as well as the interacting ones, while in the heat engine case there is a many-body advantage both in the maximum power, and in the efficiency at maximum power. Additionally, we illustrate our general results studying the paradigmatic model of a qutrit-based heat engine. Our results strictly hold in the semiclassical case in which no coherence is generated by the driving, and finally we discuss the noncommuting case.

For over six decades, quantum electrodynamics (QED) in multipolar form has been an invaluable tool for understanding quantum-scale atomic and molecular interactions. However, its relation to the Poincaré gauge has been a recent topic of controversy and debate. It was claimed by Rousseau and Felbacq in [Sci. Rep. 7, 11115 (2017)] that Hamiltonian multipolar QED is not the same as Poincaré-gauge QED and that it is not generally equivalent to Coulomb-gauge QED. This claim has subsequently been refuted, but since both sides of the debate appear technically sound, a clear reconciliation remains to be given. This task is of paramount importance due to the widespread use of multipolar QED in quantum optics and atomic physics. Here, unlike in other responses, we adopt the same method as Rousseau and Felbacq of using Dirac's constrained quantization procedure. However, our treatment shows that Poincaré-gauge and multipolar QED are identical. We identify the precise source of the apparent incompatibility of previous results as nothing more than a semantic mismatch. In fact there are no inconsistencies. Our results firmly and rigorously solidify the multipolar theory.