We present a mapping which associates pure $N$-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the number of unentangled qubits of pure $N$-qubit states.

Ultracold collisions of ions with neutral atoms in traps are studied. Recently, ultracold atom-ion systems have become available in experimental setups, where their quantum states can be coherently controlled. This control allows for an implementation of quantum information processing, combining the advantages of charged and neutral particles. The state-dependent dynamics that is a necessary ingredient for quantum computation schemes is provided in this case by the short-range interaction forces that depend on the hyperfine states of both particles. In this work, a theoretical description of spin-state-dependent trapped atom-ion collisions is developed in the framework of a multichannel quantum-defect theory and an effective single-channel model is formulated that reduces the complexity of the problem. Based on this description, a two-qubit phase gate between a ${}^{135}\mathrm{Ba}$${}^{+}$ ion and a ${}^{87}\mathrm{Rb}$ atom is simulated using a realistic combination of the singlet and triplet scattering lengths. The gate process is optimized and accelerated with the help of optimal control techniques. The result is a gate fidelity of $1-{10}^{-3}$ within $350$ $\mu$s.

A motion of a classical free charge in an electromagnetic plane wave can be found exactly in a fully relativistic case. I have found an approximate non-parametric form of the suitable equations of motion. In a linearly polarized wave, in the simplest frame of reference, the charge moves along the well-known figure-eight path. I have numerically calculated the Lorentz force acting on the charge as a function of time. By virtue of this, for the low-frequency ionization (or detachment) rate, I discuss a manifestation of nondipole and relativistic effects. When intensity of the plane wave increases, these effects can first appear in angular distributions, then in spectra of outgoing electrons, but have quite little effect on total ionization rates. I try to give an explanation of the latter fact.

Antiferromagnetism of ultracold fermions in an optical lattice can be detected by Bragg diffraction of light, in analogy to the diffraction of neutrons from solid-state materials. A finite sublattice magnetization will lead to a Bragg peak from the $(\frac{1}{2}\frac{1}{2}\frac{1}{2})$ crystal plane with an intensity depending on details of the atomic states, the frequency and polarization of the probe beam, the direction and magnitude of the sublattice magnetization, and the finite optical density of the sample. Accounting for these effects we make quantitative predictions about the scattering intensity and find that with experimentally feasible parameters the signal can be readily measured with a CCD camera or a photodiode and used to detect antiferromagnetic order.

It is shown that the one-dimensional nonlinear Schrödinger equation with a dissipative periodic potential, nonlinear losses, and a linear pump allow for the existence of stable nonlinear Bloch states which are attractors. The model describes a Bose-Einstein condensate with inelastic two- and three-body interactions loaded in an optical lattice with losses due to inelastic interactions of the atoms with photons.

A comprehensive theoretical analysis is developed for the vectorial phase conjugation using resonant four-wave mixing (FWM) in a highly degenerate rotational vibrational molecular system. The dynamic Stark shifts, saturation, and Doppler broadening are included for a realistic analysis. It is shown that the electromagnetically induced multilevel coherence controls the nonlinear wave mixing yielding interesting results for the phase conjugate (PC) reflectivity. It turns out that the efficiency of the PC reflectivity is decided by the relative phase of the Zeeman coherence and the population grating. When these two contributions are aligned in phase by a small detuning of the pump frequency, a large PC reflectivity ($~$20%) is obtained with moderate pump intensity ($~$500 mW/cm${}^2$).

The time-symmetric quantum smoothing theory [Tsang, Phys. Rev. Lett. 102, 250403 (2009); Phys. Rev. A 80, 033840 (2009)] is extended to account for discrete jumps in the classical random process to be estimated, discrete variables in the quantum system, such as spin, angular momentum, and photon number, and Poisson measurements, such as photon counting. The extended theory is used to model atomic magnetometers and study Hardy’s paradox in phase space.

We propose a time-dependent, three-dimensional numerical model where iron impurities and polarons are both considered photoactive centers to explain beam self-trapping in biased lithium niobate crystal. It shows that the intensity-dependent behavior reported experimentally is due to the competition between the drift current and the nonlinear photovoltaic current. For low light intensity, beam self-focusing occurs, while beam-splitting is observed at a higher intensity level.

A scheme is discussed for measuring $N$th-order coherences of two orthogonally polarized light fields in a single spatial mode at very limited experimental cost. To implement the scheme, the only measurements needed are the $N$th-order intensity moments after the light beam has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific settings of the wave plates. It is shown that this method can be applied for arbitrarily large $N$. A set of explicit values is given for the settings of the wave plates, constituting an optimal measurement of the $N$th-order coherences for any $N$. For Fock states the method introduced here corresponds to a full state tomography. Applications of the scheme to systems other than polarization optics are discussed.

Quantum fluctuations play a critical role in determining the steady-state and transient response of a laser when there is a small number of particles in the system. These fluctuations, and the fact that a lowest energy state of the system exists, can suppress lasing and enhance spontaneous emission around threshold. Dynamic switching between two characteristic system states can dominate the fluctuations. Correlations between $n$ discrete excited electronic states and $s$ discrete photons create a non-Poisson probability distribution and damp the average dynamic response of laser emission.

We consider the coherent propagation of $n$ photons in a one-dimensional coupled-resonator waveguide for $n=2,3,4\dots .$ The scattering by a three-level atom, which resides in one of the resonators of the waveguide and gives rise to only two-photon transitions, results in a perfect quantum switch that allows either total reflection or total transmission. This is to be contrasted to the case of a single photon inside a one-dimensional resonant waveguide scattered by a two-level system with single-photon transitions where only total reflection can be accomplished; viz. the system behaves only as a perfect mirror but not as an ideal, transparent medium.

I show relations between superposition of macroscopically distinct states and entanglement. These relations lead to the important conclusion that if a state includes superposition of macroscopically distinct states, the state also includes large multipartite entanglement in terms of several measures. Such a multipartite entanglement property also suggests that if a state includes superposition of macroscopically distinct states, a measurement on a single particle drastically changes the state of macroscopically many other particles, as in the case of the $N$-qubit Greenberger- Horne-Zeilinger state.

We report on storage of images in atomic coherences driven by electromagnetically induced transparency in a doped solid. We demonstrate image storage times up to the regime of milliseconds (i.e., more than two orders of magnitude larger than in gaseous media). Our data also reveal an improvement in the spatial resolution of the retrieved images by a factor of $40$. The long storage times become possible by applying additional radio frequency pulse sequences to drive rephasing of the atomic coherences. Moreover, the perturbing effect of atomic diffusion (which significantly limits image storage times in gases) is absent in the solid. In addition, we monitored pronounced oscillations in the intensity of the retrieved image versus the storage time. These oscillations are due to the beating of dark-state polaritons. All of these results demonstrate the superior properties of coherently driven optical data storage in solids.

We study supersymmetric (SUSY) responses to a photoassociation (PA) process in a mixture of Bose molecules $b$ and Fermi atoms $f$ which turn to mutual superpartners for a set of proper parameters. We consider the molecule $b$ to be a bound state of the atom $f$ and another Fermi atom $F$ with different species. The $b$-$f$ mixture and a free $F$ atom gas are loaded in an optical lattice. The SUSY nature of the mixture can be signaled in the response to a photon-induced atom-molecule transition: While two new types of fermionic excitations, an individual $b$ particle–$f$ hole pair continuum and the Nambu-Goldstone-fermion-like (or “goldstino-like”) collective mode, are concomitant for a generic $b$-$f$ mixture, the former is completely suppressed in the SUSY $b$-$f$ mixture and the zero-momentum mode of the latter approaches an exact eigenstate. This SUSY response can be detected by means of the spectroscopy method, for example, the PA spectrum which displays the molecular formation rate of $\mathit{Ff}\to b$.

Maxwell’s fish eye has been known to be a perfect lens within the validity range of ray optics since $1854$. Solving Maxwell’s equations, we show that the fish-eye lens in three dimensions has unlimited resolution for electromagnetic waves.

Significant achievements in high-sensitivity measurements will soon allow us to probe quantum behaviors of macroscopic mechanical oscillators. In a recent work [Phys. Rev. A 80, 043802 (2009)], we formulated a general framework for treating preparation of Gaussian quantum states of macroscopic oscillators through linear position measurements. To outline a complete procedure for testing macroscopic quantum mechanics, here we consider a subsequent verification stage which probes the prepared macroscopic quantum state and verifies the quantum dynamics. By adopting an optimal time-dependent homodyne detection in which the phase of the local oscillator varies in time, the conditional quantum state can be characterized below the Heisenberg limit, thereby achieving a quantum tomography. In the limiting case of no readout loss, such a scheme evades measurement-induced back action, which is identical to the variational-type measurement scheme invented by Vyatchanin et al. [JETP 77, 218 (1993)] but in the context for detecting gravitational waves. To motivate macroscopic quantum mechanics experiments with future gravitational-wave detectors, we mostly focus on the parameter regime where the characteristic measurement frequency is much higher than the oscillator frequency and the classical noises are Markovian, which captures the main feature of a broadband gravitational-wave detector. In addition, we discuss verifications of Einstein-Podolsky-Rosen-type entanglement between macroscopic test masses in future gravitational-wave detectors, which enables us to test one particular version of gravity decoherence conjectured by Diósi [Phys. Lett. A120, 377 (1987)] and Penrose [Gen. Rel. Grav. 28, 581 (1996)].

Magic wavelengths for laser trapping of boson isotopes of alkaline-earth metal atoms Sr, Ca, and Mg are investigated while considering terahertz clock transitions between the ${}^3{P}_0$, ${}^3{P}_1$, and ${}^3{P}_2$ metastable triplet states. Our calculation shows that magic wavelengths for laser trapping do exist. This result is important because those metastable states have already been used to make accurate clocks in the terahertz frequency domain. Detailed discussions for magic wavelengths for terahertz clock transitions are given in this article.

It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the geometric phases of its two subsystems. However, there may exist a set of states in which the nonlocal interaction does not affect the separability of the states, and the geometric phase of the bipartite system is then always equal to the sum of the geometric phases of its subsystems. In this article, we illustrate this point by investigating a well-known physical model. We give a necessary and sufficient condition in which a separable state remains separable so that the geometric phase of the system is always equal to the sum of the geometric phases of its subsystems.

One-way quantum computing is an important and novel approach to quantum computation. By exploiting the existing particle-particle interactions, we report an experimental realization of the complete process of deterministic one-way quantum Deutsch-Josza algorithm in NMR, including graph state preparation, single-qubit measurements, and feed-forward corrections. The findings in our experiment may shed light on the future scalable one-way quantum computation.

The generation of two-mode Gaussian-type entangled states of the cavity field is studied in a quantum beat laser, where three-level atoms of the $V$-type level configuration are coupled to two quantized modes of the cavity field and two upper levels of the atom are driven by a strongly classical field. According to Simon’s criterion that is a necessary and sufficient condition for the inseparability of two-mode Gaussian states with a general form of covariance matrices, we analytically and numerically investigate the influence of phase and Rabi frequency of the classical driving field, cavity loss, and the purity and nonclassicality of the initial state of the cavity field on the entanglement property of the resulting two-mode Gaussian state. In the limit of weak cavity loss and strong driving, we show that the cavity field can be periodically into an ideal two-mode entangled Gaussian-type state.