We investigate the propagation of circularly polarized electromagnetic waves through a free-standing $\mathrm{\Omega }$ particle chiral metamaterial slab and study the associated delay times: dwell time and group delay. Through this analysis, we observe different interactions of right- and left-circularly polarized waves in the terahertz frequency range (1–2.5 THz) with the resonant elements. As a consequence, the resonant-frequency group delay and dwell time of the right-circularly polarized wave are one or more orders of magnitude longer than those of the left. In addition, we compare the delay times obtained from rigorous numerical simulations with those calculated using the retrieved effective parameters. We find that the dwell time cannot be evaluated correctly from the effective medium approximation, while no such problems exist in the case of group delay.

Two- and three-mode correlation and squeezing of spontaneous parametric four-wave mixing (SPFWM) and fourth-order fluorescence (FL) composite signals are investigated theoretically and experimentally in both homonuclear (two-level) and heteronuclearlike (V-type level) molecular systems of $\mathrm{P}{\mathrm{r}}^{3+}$:YSO. By selecting different time positions, changing the power, and changing the frequency detuning of the laser field, the competition between the composite signals is demonstrated. It is found that as the laser parameters change, the signal evolves from a nonlinear ${\chi }^{\left(4\right)}$ process resulting in a FL signal to a SPFWM signal $({\chi }^{\left(3\right)}$ process). In addition, the competition effect between the signals determines the evolution of the shape of the correlation from a pure sharp to a two-stage (mixed) shape and finally to a pure broad peak amplitude. Furthermore, the signal evolution determines the magnitude of squeezing, which can control the noise level. Such progress may find potential applications in optical hybrid communication and information processing.

The goal of this paper is to elucidate the theoretical underpinnings of the metastable electronic state approach (MESA) and demonstrate its utility for the evaluation of the nonlinear optical response of noble-gas atoms with emphasis on the application of the method to the propagation of multicolor optical fields in large-scale, spatially resolved simulations. More specifically, single-active-electron models of various atoms are employed to calculate their nonlinear properties both within the adiabatic approximation, involving a single metastable state and beyond, capturing inertial effects, and wavelength-dependent ionization. Simulations for excitation pulses at different center wavelengths as well as ionization in two-color pulses are presented and compared with numerical solutions of the time-dependent Schrödinger equation. Illustrative examples of the numerical simulation of high-power pulse propagation incorporating MESA data are also presented and showcase the successful application to optical filamentation in the midinfrared region.

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Therefore, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. Here, we show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Furthermore, we propose a quantum canonical transformation that maps Hermitian systems onto non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.

We operationally introduce mixed quantum $t$-designs as the most general arbitrary-rank extension of projective quantum $t$-designs which preserves indistinguishability from the uniform distribution for $t$ copies. First, we derive upper bounds on the classical communication capacity of any mixed $t$-design measurement for $t\in [1,5]$. Second, we explicitly compute the classical communication capacity of several mixed $t$-design measurements, including the depolarized version of any qubit and qutrit symmetric, informationally complete (SIC) measurement and complete mutually unbiased bases, the qubit icosahedral measurement, the Hoggar SIC measurement, any anti-SIC (where each element is proportional to the projector on the subspace orthogonal to one of the elements of the original SIC), and the uniform distribution over pure effects.

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically nontrivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atom's position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.

We investigate, theoretically and experimentally, the properties of Fibonacci lattices with arbitrary spacings. Different from periodic structures, the reciprocal lattice and the dynamical properties of Fibonacci lattices depend strongly on the lengths of their lattice parameters, even if the sequence of long and short segment, the Fibonacci string, is the same. In this work we show that by exploiting a self-similarity property of Fibonacci strings under a suitable composition rule, it is possible to define equivalence classes of Fibonacci lattices. We show that the diffraction patterns generated by Fibonacci lattices belonging to the same equivalence class can be rescaled to a common pattern of strong diffraction peaks thus giving to this classification a precise meaning. Furthermore we show that, through the gap labeling theorem, gaps in the energy spectra of Fibonacci crystals belonging to the same class can be labeled by the same momenta (up to a proper rescaling) and that the larger gaps correspond to the strong peaks of the diffraction spectra. This observation makes the definition of equivalence classes meaningful also for the spectral and therefore dynamical and thermodynamical properties of quasicrystals. Our results apply to the more general class of quasiperiodic lattices for which similarity under a suitable deflation rule is in order.

We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.

The study of the decoherence of qubits in spin systems is almost restricted to environments whose constituents are spin-$\frac{1}{2}$ particles. In this paper we consider environments that are composed of particles of higher spin, and we investigate the consequences on the dynamics of a qubit coupled to such baths via Heisenberg $XY$ and Ising interactions. It is shown that, while the short time decay in both cases gets faster as the magnitude of the spin increases, the asymptotic behavior exhibits an improvement of the suppression of the decoherence when the coupling is through Heisenberg $XY$ interactions. In the case of a transverse Ising model, we find that the mean-field approximation breaks down for high values of the spin.

The expansion of the partition function for large coordination number $Z$ is a long-standing method and has formerly been used to describe the Ising model at finite temperatures. We extend this approach and study the interacting Bose gas at finite temperatures. An analytical expression for the free energy is derived which is valid for weakly interacting and strongly interacting bosons. The transition line which separates the superfluid phase from Mott insulating or normal gas phase is shown for fillings $\langle \widehat{n}\rangle =1$ and $\langle \widehat{n}\rangle =2$. For unit filling, our findings agree qualitatively with quantum Monte Carlo results. Contrary to the well-known mean-field result, the shift of the critical temperature in the weakly interacting regime is apparent.

We study the many-body phases of bosonic atoms with $N$ internal states confined to a one-dimensional (1D) optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The $N$ internal states of the atoms are coupled via Raman transitions creating the synthetic magnetic field in the space of internal spin states corresponding to recent experimental realizations. We focus on the case of strong $\text{SU}\left(N\right)$ invariant local density-density interactions in which each site of the 1D lattice is at most singly occupied, and strong Raman coupling, in distinction to previous work which has focused on the weak Raman coupling case. This allows us to keep only a single state per site and derive a low-energy effective spin-$1/2$ model. The effective model contains first-order nearest-neighbor tunneling terms, second-order nearest-neighbor interactions, and correlated next-nearest-neighbor tunneling terms. By adjusting the flux $\varphi$, one can tune the relative importance of first-order and second-order terms in the effective Hamiltonian. In particular, first-order terms can be set to zero, realizing a model with dominant second-order terms. We show that the resulting competition between density-dependent tunneling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-range pair-superfluid correlations. The method can be straightforwardly extended to higher dimensions and lattices of arbitrary geometry, including geometrically frustrated lattices where the interplay of frustration, interactions, and kinetic terms is expected to lead to even richer physics.

Strong coupling between cavity photons and molecular vibrations can lead to the formation of vibron-polaritons. In a recent experiment with PVAc molecules in a metal-metal microcavity [Shalabney et al., Angew. Chem., Int. Ed. 54, 7971 (2015)], such a coupling was observed to enhance the Raman scattering probability by several orders of magnitude. Inspired by this, we theoretically analyze the effect of strong photon-vibron coupling on the Raman scattering amplitude of organic molecules. This problem has recently been addressed by del Pino, Feist, and Garcia-Vidal [J. Phys. Chem. C 119, 29132 (2015)] using exact numerics for a small number of molecules. In this paper we derive compact analytic results for any number of molecules, also including the ultrastrong-coupling regime. Our calculations predict a division of the Raman signal into upper and lower polariton modes, with some enhancement to the lower polariton Raman amplitude due to the mode softening under strong coupling.

We present a comprehensive analysis of the nonlinear optical Kerr effect in graphene. We directly solve the $S$-matrix element to calculate the absorption rate, utilizing the Volkov-Keldysh-type crystal wave functions. We then convert to the nonlinear refractive index coefficients through the Kramers-Kronig relation. In this formalism, the source of Kerr nonlinearity is the interplay of optical fields that cooperatively drive the transition from valence to conduction band. This formalism makes it possible to identify and compute the rates of distinct nonlinear processes that contribute to the Kerr nonlinear refractive index coefficient. The four identified mechanisms are two-photon absorption, Raman transition, self-coupling, and quadratic ac Stark effect. We also present a comparison of our theory with recent experimental and theoretical results.

We analyze the quantum evolution represented by a time-dependent family of generalized Pauli channels. This evolution is provided by the random decoherence channels with respect to the maximal number of mutually unbiased bases. We derive the necessary and sufficient conditions for the vanishing back-flow of information.

In this paper, we argue that quantum coherence in a bipartite system can be contained either locally or in the correlations between the subsystems. The portion of quantum coherence contained within correlations can be viewed as a kind of quantum correlation which we call correlated coherence. We demonstrate that the framework provided by correlated coherence allows us to retrieve the same concepts of quantum correlations as defined by the asymmetric and symmetric versions of quantum discord as well as quantum entanglement, providing a unified view of these correlations. We also prove that correlated coherence can be formulated as an entanglement monotone, thus demonstrating that entanglement may be viewed as a specialized form of coherence.

We propose force sensing protocols using a linear ion chain which can operate beyond the quantum standard limit. We show that oscillating forces that are off resonance with the motional trap frequency can be detected very efficiently by using quantum probes represented by various spin-boson models. We demonstrate that the temporal evolution of a quantum probe described by the Dicke model can be mapped on the nonlinear Ramsey interferometry which allows us to detect far-detuned forces simply by measuring the collective spin populations. Moreover, we show that the measurement uncertainty can reach the Heisenberg limit by using initial spin-correlated states, instead of motional entangled states. An important advantage of the sensing technique is its natural robustness against the thermally induced dephasing, which extends the coherence time of the measurement protocol. Furthermore, we introduce a sensing scheme that utilizes the strong spin-phonon coupling to improve the force estimation. We show that for a quantum probe represented by the quantum Rabi model the force sensitivity can overcome the one achieved by the simple harmonic oscillator force sensor.

The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a scalable circuit QED lattice with simple realization of a universal set of nonadiabatic holonomic quantum gates. Compared with the existing proposals, we can achieve both the single and two logical qubit gates in a tunable and all-resonant way through a hybrid transmon–transmission-line encoding of the logical qubits in the decoherence-free subspaces. This distinct advantage thus leads to quantum gates with very fast speeds and consequently very high fidelities. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.

One of the simplest methods for implementing quantum key distribution over fiber-optic communication is the Bennett-Brassard 1984 protocol with phase encoding (PE-BB84 protocol), in which the sender uses phase modulation over double pulses from a laser and the receiver uses a passive delayed interferometer. Using essentially the same setup and by regarding a train of many pulses as a single block, one can carry out the so-called differential-quadrature-phase-shift (DQPS) protocol, which is a variant of differential-phase-shift (DPS) protocols. Here we prove the security of the DQPS protocol based on an adaptation of proof techniques for the BB84 protocol, which inherits the advantages arising from the simplicity of the protocol, such as accommodating the use of threshold detectors and simple off-line calibration methods for the light source. We show that the secure key rate of the DQPS protocol in the proof is eight-thirds as high as the rate of the PE-BB84 protocol.

Anonymous voting is a voting method of hiding the link between a vote and a voter, the context of which ranges from governmental elections to decision making in small groups like councils and companies. In this paper, we propose a quantum anonymous voting protocol assisted by two kinds of entangled quantum states. Particularly, we provide a mechanism of opening and permuting the ordered votes of all the voters in an anonymous manner; any party who is interested in the voting results can acquire a permutation copy and then obtains the voting result through a simple calculation. Unlike all previous quantum works on anonymous voting, our quantum anonymous protocol possesses the properties of privacy, self-tallying, nonreusability, verifiability, and fairness at the same time. In addition, we demonstrate that the entanglement of the quantum states used in our protocol makes an attack from an outside eavesdropper and inside dishonest voters impossible. We also generalize our protocol to execute the task of anonymous multiparty computation, such as anonymous broadcast and anonymous ranking.