In this paper, we theoretically demonstrate the tunability of the Casimir force both in sign and magnitude between parallel plates coated with dispersive materials. We show that this force, existing between uncharged plates, can be tuned by carefully choosing the value of the plasma frequency (i.e., the epsilon-near-zero frequency) of the coating in the neighborhood of the resonance frequency of the cavity. The coating layer enables a continuous variation of the force between four limiting values when a coating is placed on each plate. We explore the consequences of such variation when pairs of electric and magnetic conductors (i.e., low and high impedance surfaces) are used as substrates on either side, showing that this continuous variation results in changes in the sign of the force, leading to both stable and unstable conditions, which could find interesting potential applications in nanomechanics, including nanoparticle tweezing.

The Dirac equation for ${\mathrm{H}}_2^{+}$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. D 11, 15 (1989)]. The four-component wave function is expanded in a newly introduced kinetically balanced exponential basis set. The ground-state relativistic energy is obtained with an accuracy of ${10}^{-20}$, which represents an improvement by several orders of magnitude, and is shown to be in good agreement with results obtained from perturbation theory. Highly accurate relativistic wave functions are obtained, which is a first step towards nonperturbative calculations of the one-loop self-energy correction in hydrogen molecular ions.

Homogeneous quantum gases open up new possibilities for studying many-body phenomena and have now been realized for a variety of systems. For gases with short-range interactions the way to make the cloud homogeneous is, predictably, to trap it in an ideal (homogeneous) box potential. We show that creating a close to homogeneous dipolar gas in the roton regime, when long-range interactions are important, actually requires trapping particles in soft-walled (inhomogeneous) box-like potentials. In particular, we numerically explore a dipolar gas confined in a pancake trap which is harmonic along the polarization axis and a cylindrically symmetric power-law potential $r^p$ radially. We find that intermediate $p$'s maximize the proportion of the sample that can be brought close to the critical density required to reach the roton regime, whereas higher $p$'s trigger density oscillations near the wall even when the bulk of the system is not in the roton regime. We characterize how the optimum density distribution depends on the shape of the trapping potential and find it is controlled by the trap wall steepness.

An electron electric dipole moment (eEDM) search using laser-coolable triatomics such as YbOH is one of the most sensitive probes for physics beyond the standard model. The eEDM-induced energy shift is proportional to the polarization ($P$) of the molecule. Similarly to diatomics with an $\mathrm{\Omega }$-doubling structure, it was assumed that for triatomics with an $l$-doubling structure, related to the vibrational angular momentum, $P$ can be easily saturated to almost 100% with a moderate external electric field. We developed a method for the calculation of the properties of triatomic molecules and applied it to a calculation of $P$ of ${}^{174}\mathrm{YbOH}$ in the first excited $v=1$ bending mode. Calculations showed that most of the levels reach less than 50% efficiency. We showed that this fact is related to the Hund's case $b$ coupling scheme of YbOH. As the coupling scheme (for $\mathrm{\Omega }=1/2$ molecules) approaches the $a$ (or $c$) case, polarization increases up to 100%. The results of our calculations should be used for the correct extracting of the eEDM value from YbOH experiments and similar calculations are required for other molecules.

We establish and analytically derive the cutoff law for high harmonics generated with two interfering electron wave packets in the continuum. The phenomenon occurs for laser intensities high enough to spark substantial ionization, yet low enough that depletion of the ground state remains moderate to ensure a large interference yield. The continuum-continuum (CC) cutoff emerges from the maximal action difference of the dominant classical trajectories in the phase of the time-dependent dipole response. This action difference translates into an interference of a maximally time-delayed, so called stranded continuum trajectory with the trajectory of a high energy continuum electron. The time delay renders the CC harmonics more sensitive to electron wave-packet dispersion than standard high harmonics. Hence, CC harmonics should be most prominent in dimensionally reduced systems.

We study the spin-mixing dynamics of a one-dimensional strongly repulsive Fermi gas under harmonic confinement. By employing a mapping onto an inhomogeneous isotropic Heisenberg model and the symmetries under particle exchange, we follow the dynamics until very long times. Starting from an initial spin-separated state, we observe superdiffusion, spin-dipolar large amplitude oscillations, and thermalization. We report a universal scaling of the oscillations with particle number $N^{1/4}$. Our Letter puts forward one-dimensional correlated fermions as a different system to observe the emergence of nonequilibrium universal features.

We study the quantum dynamics of a one-dimensional $\mathrm{SU}(3$)-symmetric system of cold atoms in the presence of two-body losses. We exploit the representation theory of $\mathrm{SU}(3$), the so-called eightfold way, as a scheme to organize the dark states of the dissipative dynamics in terms of generalized Dicke states and show how they are dynamically approached, both in the weakly and strongly interacting and dissipative regimes. Our results are relevant for a wide class of alkaline-earth(-like) gas experiments, paving the way to the dissipative preparation and exploitation of generalized Dicke states.

We report on a scheme for laser cooling of ${}^{12}{\mathrm{C}}_2$. We have calculated the branching ratios for cycling and repumping transitions and calculated the number of photon scatterings required to achieve deflection and laser cooling of a beam of ${\mathrm{C}}_2$ molecules under realistic experimental conditions. Our results demonstrate that ${\mathrm{C}}_2$ cooling using the Swan ($d{}^3{\mathrm{\Pi }}_{\text{g}}\leftrightarrow a{}^3{\mathrm{\Pi }}_{\text{u}}$) and so-called Duck ($d{}^3{\mathrm{\Pi }}_{\text{g}}\leftrightarrow c{}^3{\mathrm{\Sigma }}_{\text{u}}^{+}$) bands is achievable via techniques similar to state-of-the-art molecular cooling experiments. The Phillips ($A{}^1{\mathrm{\Pi }}_{\text{u}}\leftrightarrow X{}^1{\mathrm{\Sigma }}_{\text{g}}^{+}$) and Ballik-Ramsay ($b{}^3{\mathrm{\Sigma }}_{\text{g}}^{-}\leftrightarrow a{}^3{\mathrm{\Pi }}_{\text{u}}$) bands offer the potential for narrow-line cooling. This work opens up a path to cooling of molecules with carbon-carbon bonds and may pave the way toward quantum control of organic molecules.

A laser with superb frequency stability plays an important role in fundamental physics research and advanced technologies. Frequency references are usually utilized to stabilize the laser, such as high-finesse cavities and atomic ensembles, of which thermal atomic beams are attractive because of their balanced performance between simplicity and stability. However, due to the transverse-velocity distribution in the thermal atomic beams, most atoms (generally $>99\%$) are wasted when interacting with the laser. Here, we propose a laser referenced on a version of velocity-grating Ramsey-Bordé atom interferometry with greatly improved atom utilization and thus superior laser frequency stability. Compared with a conventional atomic interferometry applied to stabilize the laser, the proposed system in principle generates optical Ramsey fringes with the amplitude enhanced by 1000-fold or more. Such a configuration has promising applications in diverse areas, including precision measurements and quantum metrology.

Digital quantum simulation is a promising application of quantum computers where quantum dynamics is simulated by using quantum gate operations. Many techniques for decomposing a time-evolution operator of quantum dynamics into simulatable quantum gate operations have been proposed, whereas these methods cause some errors. To evaluate these errors, we derive a lower bound for overlap between true dynamics and digital simulated dynamics at the final time. Our result enables us to guarantee how obtained digital simulated dynamics is close to unknown true dynamics. We also extend our formalism to error evaluation of digital quantum simulation on noisy quantum computers.

We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory. For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in open quantum systems. We establish that the Liouvillian describing the quantum dynamics exhibits distinct spectral features of integrable and chaotic character on the two sides of the critical point. We follow the distribution of the spacings of the complex Liouvillian eigenvalues across the critical point. In the normal and superradiant phases, the distributions are two-dimensional Poisson and that of the Ginibre unitary random matrix ensemble, respectively. Our results are corroborated by computing a recently introduced complex-plane generalization of the consecutive level-spacing ratio distribution. Our approach can be readily adapted for classifying the nature of quantum dynamics across dissipative critical points in other open quantum systems.

The complex temporal behavior of an ultrashort pulse of light propagating through a multiple scattering medium can be characterized experimentally through a time-gated transmission matrix. Using a spatial light modulator, we demonstrate here that injecting singular vectors of this matrix allows us to optimally control the energy deposition at any controllable delay time. Our approach provides insights into the fundamental aspects of multispectral light scattering and could find applications in imaging or coherent control.

The understanding of the emergence of equilibrium statistical mechanics has progressed significantly thanks to developments from typicality, canonical and dynamical, and from the eigenstate thermalization hypothesis. Here we focus on a nonequilibrium scenario in which two nonintegrable systems prepared in different states are locally and nonextensively coupled to each other. Using both perturbative analysis and numerical exact simulations of up to 28 spin systems, we demonstrate the typical emergence of nonequilibrium quasi-steady current for weak coupling between the subsystems. We also identify that these currents originate from a prethermalization mechanism, which is the weak and local breaking of the conservation of the energy for each subsystem.

When an atom is ionized by a strong laser pulse, the field can drive the released electron back to the parent ion and trigger the emission of a high-order harmonic photon with a frequency that is a function of the time of ionization. The attractive Coulomb potential causes a slowdown of the outgoing electron that must be compensated by an earlier release into the accelerating field to produce the same harmonic frequency as without the Coulomb force. By numerical solution of the time-dependent Schrödinger equation for a helium model atom, we demonstrate that such a subtle time shift of about 35 attoseconds is measurable by streaking with a weak, orthogonally polarized field combined with a complex-time trajectory interpretation. A comparison of results for high and low streaking frequency shows that only the high-frequency method measures the Coulomb shift well. This is confirmed by a classical trajectory model and by the analytical $R$-matrix theory.

We design a strategy for the real-time calibration of nuclear velocities in ultrafast molecular reactions in strong laser fields by simulating the four-dimensional time-dependent Schrödinger equation. Taking $\mathrm{H}{\mathrm{D}}^{+}$ as the prototype, an attosecond pump pulse initiates the molecular dissociation, and the other time-delayed attosecond probe pulse, polarized in the plane perpendicular to the molecular axis, ionizes the dissociating $\mathrm{H}{\mathrm{D}}^{+}$. During the dissociation, two nuclei with different masses acquire different velocities, which imprint on the photoelectron kicked off by the probe pulse. The expected photoelectron momentum along the molecular axis can be used to precisely calibrate instantaneous nuclear velocities at ionization. This strategy works widely in general heteronuclear molecules and paves the way for making high-definition molecular movies.

The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of nonstationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred to as time crystals, and they can be realized, for example, in many-body systems governed by collective dissipation and long-ranged interactions. Here, we provide a complete analytical characterization of a boundary time-crystal phase transition. This involves exact expressions for the order parameter and for the dynamics of quantum fluctuations, which, in the time-crystalline phase, remains asymptotically non-Markovian as a consequence of the time-translation symmetry breaking. We demonstrate that boundary time crystals are intrinsically critical phases, where fluctuations exhibit a power-law divergence with time. Our results show that a dissipative time-crystal phase is far more than merely a classical nonlinear and nonstationary (limit cycle) dynamics of a macroscopic order parameter. It is rather a genuine many-body phase where the properties of correlations distinctly differ from those of stationary ones.

The binding and trapping of particles usually rely on conservative forces, described by unitary quantum dynamics. We show that both can also arise solely from spatially dependent dephasing, the simplest type of decoherence. This can be based on continuous weak position measurements in only selected regions of space, for which we propose a practical realization. For a single particle, we demonstrate a quantum particle in a box based on dephasing. For two particles, we demonstrate their binding despite repulsive interactions, if their molecular states are dephased at large separations only. Both mechanisms are experimentally accessible, as we show for an example with Rydberg atoms in a cold gas background.

This Research Letter reports on the observation of superradiance decoherence caused by long-range dipole-dipole interactions between Rydberg atoms. A cold atom cloud is prepared in the mode volume of a weakly driven optical cavity and excited to a Rydberg state. The cavity transmission monitors the Rydberg dynamics in real time and detects superradiant enhancement of the transition rates between neighboring Rydberg states. The observed enhancement is reduced for increasing Rydberg atom density: a signature of atom pair interactions. The observations are explained within a model based on the idea of Rydberg blockade reducing the atom number participating in the Dicke state, responsible for superradiance.

Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples.