We derive families of optimal and near-optimal probe states for quantum estimation of the coupling constants of a general two-mode number-conserving bosonic Hamiltonian describing one-body and two-body dynamics. We find that the optimal states for estimating the dephasing of the modes, the self-interaction strength, and the contact interaction strength are related to the NOON states, whereas the optimal states for estimation of the intermode single-particle tunneling amplitude are superpositions of antipodal SU(2) coherent states. For estimation of the amplitude of pair tunneling and the amplitude of density-dependent single-particle tunneling processes, respectively, we introduce classes of variational superposition probe states that provide near perfect saturation of the corresponding quantum Cramér-Rao bounds. We show that the ground state of the pair tunneling term in the Hamiltonian has a high fidelity with the optimal states for estimation of a single-particle tunneling amplitude, suggesting that high-performance probes for tunneling amplitude estimation may be produced by tuning the two-mode system through a quantum phase transition.

We extend our recent work [Y. Endo et al., Phys. Rev. A 92, 023610 (2015)] for a parity-mixing effect in a model of two-dimensional lattice fermions to a realistic three-dimensional ultracold Fermi gas. Including effects of broken local spatial inversion symmetry by a trap potential within the framework of the real-space Bogoliubov-de Gennes theory at $T=0$, we point out that an odd-parity $p\text{-wave}$ Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) $s\text{-wave}$ superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the $s\text{-wave}$ pairing interaction to an appropriate $p\text{-wave}$ one by using a Feshbach technique in this case, a nonvanishing $p\text{-wave}$ superfluid order parameter is immediately obtained, which is given by the product of the $p\text{-wave}$ interaction and the $p\text{-wave}$ pair amplitude that has already been induced in the spin-imbalanced $s\text{-wave}$ superfluid Fermi gas. Thus, by definition, the system is in the $p\text{-wave}$ superfluid state, at least just after this manipulation. Since the achievement of a $p\text{-wave}$ superfluid state is one of the most exciting challenges in cold Fermi gas physics, our results may provide an alternative approach to this unconventional pairing state. In addition, since the parity-mixing effect cannot be explained as far as one deals with a trap potential in the local density approximation (LDA), it is considered as a crucial example which requires us to go beyond the LDA.

We propose a mechanism for the realization of exact control of parity-time $\left(\mathcal{PT}\right)$ symmetry by using a periodically modulated nonlinear optical coupler with balanced gain and loss. It is shown that for certain appropriately chosen values of the modulation parameters, we can construct a family of exact analytical solutions for the two-mode equations describing the dynamics of such nonlinear couplers. These exact solutions give explicit examples that allow us to precisely manipulate the system from nonlinearity-induced symmetry breaking to $\mathcal{PT}$ symmetry, thus providing an analytical approach to all-optical signal control in nonlinear $\mathcal{PT}$-symmetric structures.

We show that gyrotropic structures with balanced gain and loss that respect antilinear symmetries exhibit a giant nonreciprocity at the so-called exact phase where the eigenfrequencies of the isolated non-Hermitian setup are real. The effect occurs in a parameter domain near an exceptional- point (EP) degeneracy, where mode orthogonality collapses. The theoretical predictions are confirmed numerically in the microwave domain, where a nonreciprocal transport above 90 dB is demonstrated, and are further verified using lumped-circuitry modeling. The analysis allows us to speculate the universal nature of the phenomenon for any wave system where EP and gyrotropy can coexist.

We develop a simple and general method to construct arbitrary flat-band lattices. We identify the basic ingredients behind zero-dispersion bands and develop a method to construct extended lattices based on a consecutive repetition of a given miniarray. The number of degenerated localized states is defined by the number of connected miniarrays times the number of modes preserving the symmetry at a given connector site. In this way, we create one or more (depending on the lattice geometry) complete degenerated flat bands for quasi-one- and two-dimensional systems. We probe our method by studying several examples and discuss the effect of additional interactions such as anisotropy or nonlinearity. We test our method by studying numerically a ribbon lattice using a continuous description.

The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: The capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is nonconvex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.

We report a method to characterize the propagation of an ultrashort pulse of light through a multiple scattering medium by measuring its time-resolved transmission matrix. This method is based on the use of a spatial light modulator together with a coherent time-gated detection of the transmitted speckle field. Using this matrix, we demonstrate the focusing of the scattered pulse at any arbitrary position in space and time after the medium. Our approach opens different perspectives for both fundamental studies and applications in imaging and coherent control in disordered media.

We investigate theoretically the dynamical dephasing of a quantum system induced by non-Markovian noise in a nonequilibrium environment. We derive the closed equation of the dephasing factor for the quantum system under the nonstationary non-Markovian dichotomic noise environment. It is shown that the nonequilibrium feature of the environment gives rise to a time-dependent frequency shift and suppresses the dynamical dephasing of the quantum system and the environmental backaction of coherence. The memory effect of the environmental noise can reduce the dynamical dephasing of the quantum system and make the coherent backaction from the environment prominent. The non-Markovian feature of the environment, however, may not result in non-Markovian behavior in the dephasing dynamics of the quantum system.

The progress in high-precision spectroscopy requires one to verify the accuracy of theoretical models, such as the master equation describing spontaneous emission of atoms. For this purpose, we apply the coarse-graining method to derive a master equation of an atom interacting with the modes of the electromagnetic field. This master equation naturally includes terms due to quantum interference in the decay channels and fulfills the requirements of the Lindblad theorem without the need for phenomenological assumptions. We then consider the spectroscopy of the $2S-4P$ line of atomic hydrogen and show that these interference terms, typically neglected, significantly contribute to the photon count signal. These results can be important in understanding spectroscopic measurements performed in recent experiments for testing the validity of quantum electrodynamics.

Bell's theorem shows that our intuitive understanding of causation must be overturned in light of quantum correlations. Nevertheless, quantum mechanics does not permit signaling and hence a notion of cause remains. Understanding this notion is not only important at a fundamental level, but also for technological applications such as key distribution and randomness expansion. It has recently been shown that a useful way to decide which classical causal structures could give rise to a given set of correlations is to use entropy vectors. These are vectors whose components are the entropies of all subsets of the observed variables in the causal structure. The entropy vector method employs causal relationships among the variables to restrict the set of possible entropy vectors. Here, we consider whether the same approach can lead to useful certificates of nonclassicality within a given causal structure. Surprisingly, we find that for a family of causal structures that includes the usual bipartite Bell structure they do not. For all members of this family, no function of the entropies of the observed variables gives such a certificate, in spite of the existence of nonclassical correlations. It is therefore necessary to look beyond entropy vectors to understand cause from a quantum perspective.

General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this paper, we introduce a systematic method to construct a series of entropies, all of which generalize Shannon entropy in classical systems and von Neumann entropy in quantum systems. Using these entropies, the Holevo bound, an upper bound of the accessible information from a quantum system, is generalized to hold in any general probabilistic theory.

We study theoretically the responses of the dynamically corrected gates to time-dependent noises in the exchange-only spin-qubit system. We consider $1/f$ noises having spectra proportional to $1/{\omega }^{\alpha }$, where the exponent $\alpha$ indicates the strength of correlation within the noise. The quantum gate errors due to noises are extracted from a numerical simulation of randomized benchmarking and are compared between the application of uncorrected operations and that of dynamically corrected gates robust against the hyperfine noise. We have found that for $\alpha \gtrsim 1.5$, the dynamically corrected gates offer a considerable reduction in the gate error and such a reduction is approximately two orders of magnitude for the experimentally relevant noise exponent. On the other hand, no improvement of the gate fidelity is provided for $\alpha \lesssim 1.5$. This critical value of ${\alpha }_c\approx 1.5$ is larger than that for the cases for the singlet-triplet qubits. The filter transfer functions corresponding to the dynamically corrected gates are also computed and compared to those derived from uncorrected pulses. Our results suggest that the dynamically corrected gates are useful measures to suppress the hyperfine noise when operating the exchange-only qubits.

Tensor eigenvalues and eigenvectors have been introduced in the recent mathematical literature as a generalization of the usual matrix eigenvalues and eigenvectors. We apply this formalism to a tensor that describes a multipartite symmetric state or a spin state, and we investigate to what extent the corresponding tensor eigenvalues contain information about the multipartite entanglement (or, equivalently, the quantumness) of the state. This extends previous results connecting entanglement to spectral properties related to the state. We show that if the smallest tensor eigenvalue is negative, the state is detected as entangled. While for spin-1 states the positivity of the smallest tensor eigenvalue is equivalent to separability, we show that for higher values of the angular momentum there is a correlation between entanglement and the value of the smallest tensor eigenvalue.

Calculation of the differential cross section for the dielectronic recombination with two-electron uranium within the framework of QED is presented. The polarization of the emitted photon is investigated. The contributions of the Breit interaction and the interference of the photon multipoles are studied. The Breit corrections to the widths of the energy levels are taken into account and are found to be very important for both the widths and the positions of the energy levels for three-electron ions.

Ultrafast photoionization dynamics within a driver field cycle is shown to be the key to understanding the multifaceted role of the Keldysh parameter γ as the borderline between multiphoton and tunneling ionization, ionization adiabaticity degree, and a measure for the electron tunneling time. We demonstrate that, when applied to subcycle ionization dynamics, the $\gamma \ll 1$ condition automatically translates into a criterion of both adiabaticity and photoionization via tunneling. We also show that the ratio of the Keldysh γ to the frequency of the driver field indeed defines an important time scale of photoionization. However, instead of connecting to the electron motion beneath the potential barrier, it relates to the time needed for an electron to acquire a pondermotive energy equal to the ionization potential. This time scale is shown to manifest itself in the experimentally measurable buildup time of the photoelectron yield.

A binary mixture of interacting Bose-Einstein condensates (BEC) in the presence of fragmentation-driving external lattice potentials forms two interdependent mean-field lattices made of each component. These effective mean-field lattices, like ordinary optical lattices, can induce additional fragmentation and phase coherence loss of BECs between lattice sites. In this study, we consider the nonequilibrium dynamics of two hyperfine states of one-dimensional Bose-Einstein condensates, subjected to state-dependent optical lattices. Our numerical calculations using the truncated Wigner approximation (TWA) show that phase coherence in a mixture of two-component BECs can be lost not just by optical lattices, but by mean-field lattices gradually formed by other components, and we reveal that such an effect of internal mean-field lattices, however, is limited, contrary to external optical lattices, in regard to phase decoherence.

We perform a theoretical investigation into the classical and quantum dynamics of an optical field in a cavity containing a moving membrane (“membrane-in-the-middle” setup). Our approach is based on the Maxwell wave equation and complements previous studies based on an effective Hamiltonian. The analysis shows that for slowly moving and weakly reflective membranes the classical field dynamics can be approximated by first-order-in-time evolution given by an effective Schrödinger-type equation with a Hamiltonian that does not depend on the membrane speed. This approximate theory is the one typically adopted in cavity optomechanics and we develop a criterion for its validity. However, in more general situations, the full second-order wave equation predicts light dynamics which do not conserve energy, giving rise to parametric amplification (or attenuation) that is forbidden under first-order dynamics and can be considered to be the classical counterpart of the dynamical Casimir effect. The case of a membrane moving at constant velocity can be mapped onto the Landau-Zener problem, but with additional terms responsible for field amplification. Furthermore, the nature of the adiabatic regime is rather different from the ordinary Schrödinger case since mode amplitudes need not be constant even when there are no transitions between them. The Landau-Zener problem for a field is therefore richer than in the standard single-particle case. We use the work-energy theorem applied to the radiation pressure on the membrane as a self-consistency check for our solutions of the wave equation and as a tool to gain an intuitive understanding of energy pumped into or out of the light field by the motion of the membrane.

We investigate the dynamics of cavity-free lasing from neutral nitrogen molecules in femtosecond laser filaments. An important difference of intensity and temporal duration is observed between backward and forward lasing, in both amplified spontaneous emission and seed-amplification regimes. Numerical simulations based on a nonadiabatic Maxwell-Bloch model reproduce well the observations, and attribute these differences to the finite gain lifetime and the traveling excitation nature of this gas laser.

We measure a transverse momentum kick in a Sagnac interferometer using weak-value amplification with two postselections. The first postselection is controlled by a polarization-dependent phase mismatch between both paths of the interferometer, and the second postselection is controlled by a polarizer at the exit port. By monitoring the dark port of the interferometer, we study the complementary amplification of the concatenated postselections, where the polarization extinction ratio is greater than the contrast of the spatial interference. In this case, we find an improvement in the amplification of the signal of interest by introducing a second postselection to the system.