A recent experiment has observed Feshbach resonances between alkali and alkaline-earth-metal atoms. These Feshbach resonances are insensitive to the nuclear spin of alkaline-earth-metal atoms. Utilizing this feature, we propose to take this system as a candidate to perform quantum simulation of the Kondo effect. An alkali-metal atom can form a molecule with an alkaline-earth-metal atom with different nuclear spins, which plays the role of spin-exchange scattering responsible for the Kondo effect. Furthermore, we point out that the existence of three-body bound state and atom-molecule resonance due to the Efimov effect can enhance this spin-exchange scattering and therefore enhance the Kondo effect. We discuss this mechanism first with a three-body problem in free space and then demonstrate that the same mechanism still holds when the alkali-metal atom is localized by an external trap and becomes an impurity embedded in the alkaline-earth-metal atomic gases.

Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in terms of phase-space distributions. Finite dimensional systems have historically been an issue. In recent works [Phys. Rev. Lett. 117, 180401 (2016) and Phys. Rev. A 96, 022117 (2017)] we presented a framework for representing any quantum state as a complete continuous Wigner function. Here we extend this work to its partner function—the Weyl function. In doing so we complete the phase-space formulation of quantum mechanics—extending work by Wigner, Weyl, Moyal, and others to any quantum system. This work is structured in three parts. First we provide a brief modernized discussion of the general framework of phase-space quantum mechanics. We extend previous work and show how this leads to a framework that can describe any system in phase space—putting it for the first time on a truly equal footing to Schrödinger's and Heisenberg's formulation of quantum mechanics. Importantly, we do this in a way that respects the unifying principles of “parity” and “displacement” in a natural broadening of previously developed phase-space concepts and methods. Secondly we consider how this framework is realized for different quantum systems; in particular we consider the proper construction of Weyl functions for some example finite dimensional systems. Finally we relate the Wigner and Weyl distributions to statistical properties of any quantum system or set of systems.

A composite quantum channel is derived for two independent quantum systems that interact sequentially with a common environment. One of the two quantum systems first interacts with the environment for a finite time, and after that the other one interacts with the same environment. In the process, the environment does not simultaneously interact with the two quantum systems. It is important to note that the second quantum system interacts with the environment that has been disturbed by the first one. As a result, the correlation between the two quantum systems, not directly interacting with each other, is created through the environment. An approximation to the composite quantum channel is also provided, which is applicable if a correlation time of the environment is not so long. When two independent qubits interact sequentially with a common bosonic environment via a dephasing coupling, it is explicitly shown that the time evolution of the second qubit can be non-Markovian due to the disturbance effect caused by the first qubit, even if the time evolution of the first qubit is Markovian. Entanglement, total, classical, and quantum correlations are calculated to find how the disturbance affects bipartite correlations. Furthermore, in state transmission through the composite quantum channel, it is found that the fidelity of quantum states can be enhanced by the disturbance effect.

We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domainwise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard-wall boundaries leads to extrema of the eigenenergies. The underlying wave function becomes then an eigenstate of the local symmetry transform in each of the domains of local symmetry. These extrema accumulate towards eigenenergies which do not depend on the position of the potentials inside the walls. They correspond to perfect transmission resonances of the associated scattering setup, obtained by removing the hard walls. We argue that this property characterizes the duality between scattering and bounded systems in the presence of local symmetries. Our findings are illustrated through a numerical example with a potential consisting of two domains of local symmetry, each comprised of Dirac $\delta$ barriers.

According to the eigenstate thermalization ansatz, matrices representing generic few-body observables take on a specific form when displayed in the eigenbasis of a chaotic Hamiltonian. We examine the effect of environment-induced decoherence on the dynamics of observables that conform with said eigenstate thermalization ansatz. The obtained result refers to a description of the dynamics in terms of an integro-differential equation of motion of the Nakajima-Zwanzig form. We find that environmental decoherence is equivalent to an exponential damping of the respective memory kernel. This statement is formulated as a rigorous theorem. Furthermore, the implications of the theorem on the stability of exponential dynamics against decoherence and the transition towards Zeno freezing are discussed.

We propose an efficient method for generating two-mode squeezed states of the collective excitation of two nitrogen-vacancy-center ensembles (NVEs), which are magnetically coupled to two interacting superconducting transmission line resonators via photon hopping, respectively. By applying the external driving fields to induce Raman transitions between the ground-state sublevels of the nitrogen-vacancy center, an effective interaction between the spin ensembles and the resonators can be engineered. We show that the dissipative quantum dynamical process of the two resonators can be employed to steer the two NVEs into a two-mode squeezed state. By comparison with previous proposals, our scheme does not need either an extra superconducting qubit, or external squeezing resource. The present work may have potential applications for implementing NVE-based hybrid quantum computation.

By considering an unreliable oracle in a query-based model of quantum learning, we present a tradeoff relation between the oracle's reliability and the reusability of the quantum state of the input data. The tradeoff relation manifests as the fundamental upper bound on the reusability. This limitation on the reusability would increase the quantum access to the input data, i.e., the usage of quantum random access memory (qRAM), repeating the preparation of a superposition of large (or big) input data on the query failure. However, it is found that a learner can obtain a correct answer even from an unreliable oracle without any additional usage of qRAM; i.e., the complexity of the qRAM query does not increase even with an unreliable oracle. This is enabled by repeatedly cycling the quantum state of the input data to the upper bound on the reusability.

We revisit the problem of detection of entanglement of an unknown two-qubit state using minimal resources. Using weak values and just two copies of an arbitrary two-qubit state, we present a protocol where a postselection measurement in the computational basis provides enough information to identify if the state is entangled or not. Our protocol enables complete state identification with a single-setting postselection measurement on two copies of the state. It follows that by restricting to pure states, the global interaction required for determining the weak values can be realized by local operations. We further show that our protocol is robust against errors arising from inappropriate global interactions applied during weak value determination.

Antihydrogen atoms are routinely formed at CERN in a broad range of Rydberg states. Ground-state antiatoms, those useful for precision measurements, are eventually produced through spontaneous decay. However given the long lifetime of Rydberg states the number of ground-state antihydrogen atoms usable is small, in particular for experiments relying on the production of a beam of antihydrogen atoms. Therefore, it is of high interest to efficiently stimulate the decay in order to retain a higher fraction of ground-state atoms for measurements. We propose a method that optimally mixes the high angular momentum states with low ones enabling us to stimulate, using a broadband frequency laser, the deexcitation toward low-lying states, which then spontaneously decay to the ground state. We evaluate the method in realistic antihydrogen experimental conditions. For instance, starting with an initial distribution of atoms within the $n=20–30$ manifolds, as formed through the charge exchange mechanism, we show that more than 80% of antihydrogen atoms will be deexcited to the ground state within 100 ns using a laser producing 2 J at 828 nm.

We present an analytical and numerical solution of the calculation of the transition moments for the exact semiclassical light-matter interaction for wave functions expanded in a Gaussian basis. By a simple manipulation we show that the exact semiclassical light-matter interaction of a plane wave can be compared to a Fourier transformation of a Gaussian where analytical recursive formulas are well known and hence, making the difficulty in the implementation of the exact semiclassical light-matter interaction comparable to the transition dipole. Since the evaluation of the analytical expression involves a new Gaussian, we instead have chosen to evaluate the integrals using a standard Gauss-Hermite quadrature, since this is faster. A brief discussion of the numerical advantages of the exact semiclassical light-matter interaction in comparison to the multipole expansion along with the unphysical interpretation of the multipole expansion is discussed. Numerical examples on $[{\mathrm{CuCl}}_4{]}^{2-}$ show that the usual features of the multipole expansion are immediately visible also for the exact semiclassical light-matter interaction and that this can be used to distinguish between symmetries. Calculation on $[{\mathrm{FeCl}}_4{]}^{1-}$ is presented to demonstrate the better numerical stability with respect to the choice of basis set in comparison to the multipole expansion and finally, Fe-O-Fe to show origin independence is a given for the exact operator. The implementation is freely available in OpenMolcas.

When optically pumped magnetometers are aimed for use in the Earth's magnetic field, the orientation of the sensor to the field direction is of special importance to achieve accurate measurement results. Measurement errors and inaccuracies related to the heading of the sensor can be an even more severe problem in the case of special operational configurations, such as the use of strong off-resonant pumping. We systematically study the main contributions to the heading error in systems that promise high magnetic field resolutions at the Earth's magnetic field strengths, namely the nonlinear Zeeman splitting and the orientation-dependent light shift. The good correspondence of our theoretical analysis to experimental data demonstrates that both of these effects are related to a heading-dependent modification of the interaction between the laser light and the dipole moment of the atoms. Also, our results promise a compensation of both effects using a combination of clockwise and counterclockwise circular polarization.

We investigated the core-filling properties of dark solitons in one-dimensional spin-orbit-coupled Fermi gases. Majorana fermions can exist at the edges of the topological superfluid, when the spin-orbit coupling drives this system from the superfluid to the topological superfluid. Our results show that when dark solitons participate, the state of the system and the existence of Majorana zero-energy modes at the edges of topological superfluid correlate with the filling status of the core of the dark soliton. Furthermore, this dark soliton can actually accommodate two extra Majorana excitations without interactions in its core, when it is filled with highly imbalanced spins in a specific region of parameters. These features can be utilized to manipulate Majorana fermions in the topological superfluid.

Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly bound $N$-body clusters consisting of $N-1$ identical bosons (denoted by “B”) of mass $m$ that interact with a single distinguishable impurity particle (denoted by “X”) of mass $M$. The system properties are analyzed as a function of the mass ratio $\kappa$ (values from $\kappa =1$ to 50 are considered), where $\kappa$ is equal to $m/M$, and the two-body $s$-wave scattering length $a_{\text{BX}}$ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.

Precise knowledge of optical lattice depths is important for a number of areas of atomic physics, most notably in quantum simulation, atom interferometry, and for the accurate determination of transition matrix elements. In such experiments, lattice depths are often measured by exposing an ultracold atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the fraction of atoms found in each of the allowed momentum states by time-of-flight measurement, after some number of pulses. We present a full analytic model for the time evolution of the atomic populations of the lowest momentum states, which is sufficient for a “weak” lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices. Finally, we consider the situation where the initial gas is explicitly assumed to be at a finite temperature.

We study a qubit-oscillator system, with a time-dependent coupling coefficient, and present a fast scheme for generating entangled Schrödinger-cat states with large mean photon numbers and also a scheme that protects the cat states against dephasing caused by the nonlinearity in the system. We focus on the case where the qubit frequency is small compared to the oscillator frequency. We first present the exact quantum state evolution in the limit of infinitesimal qubit frequency. We then analyze the first-order effect of the nonzero qubit frequency. Our scheme works for a wide range of coupling strength values, including the recently achieved deep-strong-coupling regime.

The evolution of classical optical fields propagating through atmospheric turbulence is investigated under arbitrary conditions. We use the single-phase screen (SPS) method and the infinitesimal propagation equation (IPE), a multiphase screen (MPS) method, to compute the optical power fractions retained in an input Laguerre-Gauss (LG) mode or transferred to higher-order LG modes. Although they show the same trend while the scintillation is weak, the IPE and SPS predictions deviate when the strength of scintillation passes a certain threshold. These predictions are compared with numerical simulations of optical fields propagating through turbulence. The simulations are performed using an MPS model, based on the Kolmogorov theory of turbulence, for different turbulence conditions to allow comparison in both weak and strong scintillation. The numerical results agree well with the IPE results in all conditions, but they deviate from the SPS results for strong scintillation.

The time delay and absorption of ultrashort electromagnetic pulses are defined from the local maximum of the wave's electric field and envelope. A time-domain framework is derived to obtain, in dispersive and absorbing linear media, the expressions of the phase and group time delays, and of the absorption undergone by the wave. These expressions are related to the dielectric properties of the medium but also to the local curvature of the wave's electric field. The result provides a unified and rational picture of the propagation, in dispersive and absorbing media, of ultrashort electromagnetic pulses in transmission and attenuated total reflection (ATR) geometries.

Unlike a Chern number in a two-dimensional $(2\mathrm{D})$ and $3\mathrm{D}$ topological system, the Zak phase takes a subtle role to characterize the topological phase in $1\mathrm{D}$. On the one hand, it is not gauge invariant, and, on the other hand, the Zak phase difference between two quantum phases can be used to identify the topological phase transitions. A non-Hermitian system may inherit some characters of a Hermitian system, such as entirely real spectrum, unitary evolution, topological energy band, etc. In this paper, we study the influence of a non-Hermitian term on the Zak phase. We show exactly that the real part of the Zak phase remains unchanged in a class of $1\mathrm{D}$ bipartite lattice systems even in the presence of the on-site imaginary potential. The non-Hermitian term only gives rise to the imaginary part of Zak phase. Such a complex quantity has a physical implication when we consider the dynamical realization in which the Zak phase can be obtained through adiabatic evolution. In this context, its imaginary part represents the amplification and/or attenuation of the Dirac norm of the evolved state. Based on this finding, we investigate a scattering problem for a time-dependent scattering center, which is a magnetic-flux-driven non-Hermitian Su-Schrieffer-Heeger ring. Due to the topological nature of the Zak phase, the intriguing features of this design are the wave-vector independence and allow two distinct behaviors, perfect transmission or confinement, depending on the timing of a flux impulse threading the ring. When the flux is added during a wave packet travelling within the ring, the wave packet is confined in the scatter partially. Otherwise, it exhibits perfect transmission through the scatter. Our finding extends the understanding and broadens the possible application of the Zak phase in a non-Hermitian system.