We present the realization of a Stückelberg interferometer with two mechanical modes in a two-coupled-cantilever–based optomechanical system. By optically tuning the frequency of one cantilever inside a cavity, we show that nonadiabatic crossing of the mechanical modes twice creates the interference fringes of the mechanical oscillations as a result of coherent splitting and subsequent recombination of the oscillations. By measuring the nonadiabatic phase acquired at the transition, we unveil an in-depth analog between the two-mode and quantum two-level systems. With this interferometry-based technique, transferring of oscillation between spatially separated cantilevers is achieved with 97% efficiency.

We demonstrate coherent control of the rotational and hyperfine state of ultracold, chemically stable ${}^{87}\mathrm{Rb}{}^{133}\mathrm{Cs}$ molecules with external microwave fields. We create a sample of $\sim 2000$ molecules in the lowest hyperfine level of the rovibronic ground state $N=0$. We measure the transition frequencies to eight different hyperfine levels of the $N=1$ state at two magnetic fields $\sim 23$ G apart. We determine accurate values of rotational and hyperfine coupling constants that agree well with previous calculations. We observe Rabi oscillations on each transition, allowing complete population transfer to a selected hyperfine level of $N=1$. Subsequent application of a second microwave pulse allows the transfer of molecules back to a different hyperfine level of $N=0$.

Despite being ubiquitous, out-of-equilibrium quantum systems are much less understood than systems at equilibrium. Progress in the field has benefited from a symbiotic relationship between theoretical studies and new experiments on coherent dynamics. The present work strengthens this connection by providing a general picture of the relaxation process of isolated lattice many-body quantum systems that are routinely studied in experiments with cold atoms, ions traps, and nuclear magnetic resonance. We show numerically and analytically that the long-time decay of the probability for finding the system in its initial state necessarily shows a power-law behavior $\propto t^{-\gamma }$. This happens independently of the details of the system, such as integrability, level repulsion, and the presence or absence of disorder. Information about the spectrum, the structure of the initial state, and the number of particles that interact simultaneously is contained in the value of $\gamma$. From it, we can anticipate whether the initial state will or will not thermalize.

Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where environment-mediated transitions introduce additional decoherence channels. Adiabatic passage is a well-established solution but requires a sufficiently slow evolution time that is dictated by the adiabatic theorem. Here we develop a systematic projection theory formulation for the transitionless evolution of general open quantum systems described by time-local master equations. We derive a time-convolutionless dynamical equation for the target instantaneous eigenstate of a given time-dependent Hamiltonian. A transitionless dynamics then arises in terms of a competition between the average Hamiltonian gap and the decoherence rate, which implies optimal adiabaticity timescales. We show how eigenstate tracking can be accomplished via control pulses, without explicitly incorporating counter-diabatic driving, thus offering an alternative route to accelerate adiabaticity. We examine rectangular pulses, chaotic signals, and white noise, and find that, remarkably, the effectiveness of eigenstate tracking hardly depends on the details of the control functions. In all cases the control protocol keeps the system in the desired instantaneous eigenstate throughout the entire evolution, along an accelerated adiabatic path.

Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve nonzero power for the practical extraction of work, these processes must be performed within a finite time, which inevitably induces excitations in the system. We show that depending on the time scale of the process and the physical realization of the external driving employed, the use of counterdiabatic quantum driving to extract more work is not always effective. We also show that by virtue of the two-time energy measurement definition of quantum work, the cost of counterdiabatic driving can be significantly reduced by selecting a restricted form of the driving Hamiltonian that depends on the outcome of the first energy measurement. Lastly, we introduce a measure, the exigency, that quantifies the need for an external driving to preserve quantum adiabaticity which does not require knowledge of the explicit form of the counterdiabatic drivings, and can thus always be computed. We apply our analysis to systems ranging from a two-level Landau-Zener problem to many-body problems, namely, the quantum Ising and Lipkin-Meshkov-Glick models.

The accurate detection of small deviations in given density matrice is important for quantum information processing, which is a difficult task because of the intrinsic fluctuation in density matrices reconstructed using a limited number of experiments. We previously proposed a method for decoherence error detection using a machine-learning technique [S. Hara, T. Ono, R. Okamoto, T. Washio, and S. Takeuchi, Phys. Rev. A 89, 022104 (2014)]. However, the previous method is not valid when the errors are just changes in phase. Here, we propose a method that is valid for arbitrary errors in density matrices. The performance of the proposed method is verified using both numerical simulation data and real experimental data.

For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs and passive elements, by calculating the covariance matrix. The quantum Cramér-Rao bound provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We prove that this bound can be saturated. In spite of the Gaussian nature of the problem, the calculation of non-Gaussian integrals is required, which we accomplish analytically. We find our simultaneous strategy to yield no more than a factor-of-2 improvement in total precision, possibly because of a fundamental performance limitation of Gaussian states. Our work shows that no modal entanglement is necessary for simultaneous quantum-enhanced estimation of multiple phases.

Spin state and open-shell character dependences of the static second hyperpolarizability (γ) are theoretically investigated using hydrogen chain models ${\mathrm{H}}_{2n}\left(1\le n\le 3\right)$ at the full configuration interaction level of approximation. The variation in γ is examined as a function of changing the spin state for a variety of open-shell characters ranging from the closed-shell to pure open-shell states. It is found that (i) in the nearly ground-state closed-shell region, higher-spin states exhibit much larger γ values than the singlet state; (ii) in the intermediate and large open-shell character regions, the singlet state presents the largest γ and γ decreases with the spin multiplicity; and (iii) in the pure open-shell region, all the spin states exhibit negligible γ values. The summation-over-states approach enables rationalizing these findings by considering the primarily contributing excited states. These results reveal that there are two types of molecular design guidelines for enhancing γ values: (a) for nearly closed-shell systems, increasing the spin multiplicity; and (b) for open-shell singlet systems, tuning the open-shell character to the intermediate region.

Rydberg atoms possess a strong atom-atom interaction, which limits its density in an atomic sample. Such effect is known as a Rydberg-atom blockade. Here, we present a way to control such effect by directly orienting the induced atomic dipole moment using a dc external electrical field. To demonstrate it, we excite the $50S_{1/2}$ Rb atomic state in a quasiunidimensional sample held in a quasielectrostatic trap. A pure $nS$ state holds only van der Waals interaction at long range, but in the presence of an external electric field the state mixing leads to strong dipole-dipole interactions. We have measured the Rydberg-atom population as a function of ground-state atoms density for several angles between the electric field and the main axis of the unidimensional sample. The results indicate that the limit on the final Rydberg density can be controlled by electric-field orientation. Besides, we have characterized the sample by using a single-atom ion imaging technique, demonstrating that it does behave as a unidimensional sample.

The photoelectron momentum distributions (PMDs) of the hydrogen molecular ion ${\mathrm{H}}_2{}^{+}$ driven by strong near-infrared laser pulses are studied based on the ab initio numerical solution of the time-dependent Schrödinger equation and the Volkov wave propagation. Both linear and circular polarization are considered, in accordance with the recent experiment by M. Odenweller et al. [Phys. Rev. A 89, 013424 (2014)]. We will discuss the difference between the molecular (diatomic) and the atomic PMDs and the effect of molecular potential to the photoelectron energy. In particular, we demonstrate that the above-threshold ionization spectra of ${\mathrm{H}}_2{}^{+}$ could upshift their energy when driven by a linearly polarized laser field parallel to the molecular axis.

We show that unidirectional propagation of light rays in the limit of geometric optics could arise in some magnetic fluids due to the magnetoelectric effect under weak DC magnetic fields and strong DC electric fields around half of their dielectric breakdown. For such liquids as kerosene and transformer oils, one-way propagation of light may occur for 30-nm-diameter magnetic nanoparticles (e.g., cobalt) and concentrations of $2\%$ or larger.

We describe linear and nonlinear modes in a ring-shaped waveguide with localized gain and dissipation modeled by two Dirac $\delta$ functions located symmetrically. The strengths of the gain and dissipation are equal, i.e., the system obeys the parity-time symmetry. This configuration describes atomic Bose-Einstein condensates with local loading and local elimination of atoms, polaritonic condensates, or optical ring resonators with local pump and absorption. We discuss the linear spectrum of such a system and show that if the location of the $\delta$ functions is slightly asymmetric, then the system can be driven through a series of exceptional points by the change of the gain-and-loss coefficient. In the nonlinear case, the system admits solutions with spatially constant and periodic densities which are presented in the exact analytical form. These solutions are supported by the current directed from the gain potential towards the absorbing potential. The system also admits currentless solutions. Stability and bifurcations of nonlinear solutions are also described.

Laguerre-Gaussian (LG) light modes with large values of the radial index $p$ and the azimuthal index $l$ are considered. We give special emphasis on the mechanical effects on atoms arising from the Gouy phase and the phase due to the curvature of such light. It is shown that the additional phase terms for highly twisted light can lead to mechanical effects based on the substantial reduction of the axial wavenumber. As a consequence, axial recoil effects are diminished in the processes of stimulated emission and absorption of the light by the atoms. Both the scattering force and the momentum diffusion are affected by the inclusion of these normally ignored additional phase terms. The magnitudes of the effects are explored using order of magnitude analysis with typical parameters due to the atoms and the light.

We investigate $\mathcal{P}\mathcal{T}$-symmetric quantum systems ultraweakly coupled to an environment. We find that such open systems evolve under $\mathcal{P}\mathcal{T}$-symmetric, purely dephasing and unital dynamics. The dynamical map describing the evolution is then determined explicitly using a quantum canonical transformation. Furthermore, we provide an explanation of why $\mathcal{P}\mathcal{T}$-symmetric dephasing-type interactions lead to a critical slowing down of decoherence. This effect is further exemplified with an experimentally relevant system, a $\mathcal{P}\mathcal{T}$-symmetric qubit easily realizable, e.g., in optical or microcavity experiments.

We describe an experimentally feasible protocol for performing a variant of the quantum delayed-choice experiment with massive objects. In this scheme, a single nitrogen-vacancy (NV) center in diamond driven by microwave fields is dispersively coupled to a massive mechanical resonator. A double-pulse Ramsey interferometer can be implemented with the spin-mechanical setup, where the second Ramsey microwave pulse drives the spin conditioned on the number states of the resonator. The probability for finding the NV center in definite spin states exhibits interference fringes when the mechanical resonator is prepared in a specific number state. On the other hand, the interference is destroyed if the mechanical resonator stays in some other number states. The wavelike and particlelike behavior of the NV spin can be superposed by preparing the mechanical resonator in a superposition of two distinct number states. Thus a quantum version of Wheeler's delayed-choice experiment could be implemented, allowing fundamental tests of quantum mechanics on a macroscopic scale.

We present dichroism measurements in molecules prealigned with a short and intense laser pulse, using a balanced detection and a pump-probe scheme. The birefringence signal is recorded under the same irradiation conditions along with the dichroism one. Our results show that the dichroism signal is of comparable order of magnitude as the one originating from birefringence and reflects the degree of alignment. The balanced detection scheme directly provides an heterodyne signal for both birefringence and dichroism. Experiments are first conducted in air and then in pure nitrogen and carbon dioxide gases. A general approach allows us to explain the temporal shape of the dichroic response and to extract the imaginary part of the polarizability anisotropy. Furthermore, a simple model invoking the finite response time of the molecule to the probe excitation provides a complementary perspective. Using this model, the phase shift between the oscillations of the probe electric field and the induced polarization can be estimated. We find that the phase shift corresponds to a time delay of about 130 as $({\displaystyle {10}^{-18}}$ s) in both molecules. Calculation of the energy flow between the probe field and the molecules taking into account the phase shift is compared to the experimental data.

Strong-field photoemission and electron recollision provide a viable route to extract electronic and nuclear dynamics from molecular targets with attosecond temporal resolution. However, since an ab initio treatment of even the simplest diatomic systems is beyond today's capabilities, approximate qualitative descriptions are warranted. In this paper, we develop such a theoretical approach to model the photoelectrons resulting from intense laser-molecule interaction. We present a general theory for symmetric diatomic molecules in the single active electron approximation that, amongst other capabilities, allows adjusting both the internuclear separation and molecular potential in a direct and simple way. More importantly, we derive an analytic approximate solution of the time-dependent Schrödinger equation (TDSE), based on a generalized strong-field approximation (SFA) version. Using that approach, we obtain expressions for electron emitted transition amplitudes from two different molecular centers, and accelerated then in the strong laser field. In addition, our approach directly underpins different underlying physical processes that correspond to (i) direct tunneling ionization; (ii) electron rescattering on the center of origin; and, finally, (iii) electron rescattering on a different center. One innovative aspect of our theory is the fact that the dipole matrix elements are free from nonphysical gauge and coordinate system-dependent terms: this is achieved by adapting the coordinate system, in which SFA is performed, to the center from which the corresponding part of the time-dependent wave function originates. Our analytic results agree very well with the numerical solution of the full three-dimensional TDSE for the ${{\mathrm{H}}_2}^{+}$ molecule. Moreover, the theoretical model was applied to describe laser-induced electron diffraction measurements of ${{\mathrm{O}}_2}^{+}$ molecules, obtained at ICFO, and reproduces the main features of the experiment very well. Our approach can be extended in a natural way to more complex molecules and multielectron systems.

Using exact Bethe ansatz solutions, we show that a spin-down fermion immersed into a fully polarized spin-up Fermi sea with a weak attraction is dressed by the surrounding spin-up fermions to form the one-dimensional analog of a polaron. As the attraction becomes strong, the spin-down fermion binds with one spin-up fermion to form a tightly bound molecule. Throughout the whole interaction regime, a crossover from the polaron to a molecule state is fully demonstrated through exact results of the excitation spectrum, the effective mass, binding energy and kinetic energy. Furthermore, a clear distinction between the polaron and molecule is conceived by the probability distribution, single-particle reduced density matrix, and density-density correlations, which are calculated directly from the Bethe ansatz wave function. Such a polaron-molecule crossover presents a universal nature of an impurity immersed into a fermionic medium with an attraction in one dimension.