Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. We apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with a high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.

Methods for precisely resolving the continuous-variable energy-time entanglement of paired photons have always been sought in quantum optics. The Fabry-Pérot interferometer provides such a distinguished opportunity if the single-photon pulse's self-interference is carefully avoided. A dual-channel Fabry-Pérot interferometer is proposed and studied with the focus put upon higher-order quantum interference effects. When the two channels are properly set up, the interferometer is capable of resolving the energy-time entanglement in detail, similar to how the usual Fabry-Pérot interferometer can resolve classical light's spectrum. A variation form of the dual-channel Fabry-Pérot interferometry is also discussed.

M. Pirbhai et al. [Phys. Rev. A 88, 060701(R) (2013)] reported a new optically pumped spin-exchange polarized-electron source developed to avoid the limitations of the traditional GaAs-type source and to enable a broader range of experiments. The spin-exchange gaseous source has introduced its own limitations with 650-mW laser power producing only $4\mu \mathrm{A}$ of spin-polarized current with a 24% polarization and a 2-eV energy spread depending markedly on tenuous roles of various buffer gases which we consider are not explained cogently. Spin-related beam experiments over many decades have significant achievements using GaAs spin sources.

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Enhanced nonlinear optical response of a coherent atomic medium is the basis for many atomic sensors, and their performance is ultimately limited by the quantum fluctuations of the optical readout. Here we demonstrate that the off-resonant interactions, with the aid of the near-resonant process, can significantly modify the quantum noise of a coherent light field, even when its effect on the mean signal is negligible. The altered quantum optical noise distribution results in excess noise in the measurement quantity. We illustrate this concept by using an atomic magnetometer based on the nonlinear Faraday effect. These results show the existence of previously unnoticed factors in fundamental limitations in atomic magnetometry and could have impact in a wide range of atom-light–based precision measurements.

Quantum coherence is a key element in topical research on quantum resource theories and a primary facilitator for design and implementation of quantum technologies. However, the resourcefulness of quantum coherence is severely restricted by environmental noise, which is indicated by the loss of information in a quantum system, measured in terms of its purity. In this work, we derive the limits imposed by the mixedness of a quantum system on the amount of quantum coherence that it can possess. We obtain an analytical trade-off between the two quantities that upperbound the maximum quantum coherence for fixed mixedness in a system. This gives rise to a class of quantum states, “maximally coherent mixed states,” whose coherence cannot be increased further under any purity-preserving operation. For the above class of states, quantum coherence and mixedness satisfy a complementarity relation, which is crucial to understand the interplay between a resource and noise in open quantum systems.

We address the question of locality versus nonlocality in the Aharonov-Bohm and the Aharonov-Casher effects. For this purpose, we investigate all possible configurations of ideal shielding of the overlap between the electromagnetic fields generated by a charge and by a magnetic flux and analyze their consequences on the Aharonov-Bohm-Casher interference. In a classical treatment of shielding, the Aharonov-Bohm-Casher effect vanishes regardless of the geometry of shielding when the local overlap of electromagnetic fields is completely eliminated. On the other hand, the result depends on the configuration of shielding if the charge quantization in the superconducting shield is taken into account. It is shown that our results are fully understood in terms of the fluctuating local-field interaction. Our analysis strongly supports the alternative view on the Aharonov-Bohm-Casher interference that the effects originate from the local action of electromagnetic fields.

We investigate the geometric phase for a quantum field driven by an external source and subjected to spontaneous decay from coupling to the reservoir. Starting from a coherent state, we analyze the effect of decoherence when the system undergoes a nonadiabatic cyclic evolution in phase space, and show that the lowest correction to the conventional geometric phase is quadratic in the decaying rate of the quantum field. This is in distinct contrast with the nonadiabatic geometric phase associated with the evolution of a spin system subjected to spontaneous decay, which contains the first-order correction term. We further show that the unconventional geometric phase is also robust to field decay.

Many important computer science problems can be reduced to the clause-satisfaction problem. We are given $n$ Boolean variables $x_k$ and $m$ clauses $c_j$ where each clause is a function of values of some $x_k$. We want to find an assignment $i$ of $x_k$ for which all $m$ clauses are satisfied. Let $f_j\left(i\right)$ be a binary function, which is 1 if the $j\mathrm{th}$ clause is satisfied by the assignment $i$, else $f_j\left(i\right)=0$. Then the solution is $r$ for which $f(i=r)=1$, where $f\left(i\right)$ is the and function of all $f_j\left(i\right)$. In quantum computing, Grover's algorithm can be used to find $r$. A crucial component of this algorithm is the selective phase inversion $I_r$ of the solution state encoding $r$. $I_r$ is implemented by computing $f\left(i\right)$ for all $i$ in superposition which requires computing and of all $m$ binary functions $f_j\left(i\right)$. Hence there must be coupling between the computation circuits for each $f_j\left(i\right)$. In this paper, we present an alternative quantum search algorithm which relaxes the requirement of such couplings. Hence it offers implementation advantages for clause-satisfaction problems.

On top of the mean-field analysis of a Bose-Einstein condensate, one typically applies the Bogoliubov theory to analyze quantum fluctuations of the excited modes. Therefore, one has to diagonalize the Bogoliubov Hamiltonian in a symplectic manner. In our article we investigate the topology of these Bogoliubov excitations in inversion-invariant systems of interacting bosons. We analyze how the condensate influences the topology of the Bogoliubov excitations. Analogously to the fermionic case, here we establish a symplectic extension of the polarization characterizing the topology of the Bogoliubov excitations and link it to the eigenvalues of the inversion operator at the inversion-invariant momenta. We also demonstrate an instructive but experimentally feasible example that this quantity is also related to edge states in the excitation spectrum.

The tight confinement of the evanescent light field around the waist of an optical nanofiber makes it a suitable tool for studying nonlinear optics in atomic media. Here, we use an optical nanofiber embedded in a cloud of laser-cooled ${}^{87}\mathrm{Rb}$ for near-infrared frequency up-conversion via a resonant two-photon process. Sub-nW powers of the two-photon radiation, at 780 and 776 nm, copropagate through the optical nanofiber and the generation of 420 nm photons is observed. A measurement of the Autler-Townes splitting provides a direct measurement of the Rabi frequency of the 780 nm transition. Through this method, dephasings of the system can be studied. In this work, the optical nanofiber is used as an excitation and detection tool simultaneously, and it highlights some of the advantages of using fully fibered systems for nonlinear optics with atoms.

We use theoretical analysis and numerical simulation to investigate the operation of a laser oscillating from gain supplied by stimulated Brillouin scattering (SBS) in a microresonator. The interaction of the forward, backward, and density waves within the microresonator results in a set of coupled-mode equations describing both the laser's phase and amplitude evolution over time. Using this coupled-mode formalism, we investigate the performance of the SBS laser under noise perturbation and identify the fundamental parameters and their optimization to enable low-noise SBS operation. The intrinsic laser linewidth, which is primarily limited by incoherent thermal occupation of the density wave, can be of order hertz or below. Our analysis also determines the SBS laser's relaxation oscillation, which results from the coupling between the optical and density waves, and appears as a resonance in both the phase and amplitude quadratures. We further explore contributions of the pump noise to the SBS laser's performance, which we find under most circumstances to increase the SBS laser noise beyond its fundamental limits. By tightly stabilizing the pump laser onto the microcavity resonance, the transfer of pump noise is significantly reduced. Our analysis is both supported and extended through numerical simulations of the SBS laser.

Quantum optical fields offer numerous control knobs which are not available with classical light and may be used for monitoring the properties of matter by novel types of spectroscopy. It has been recently argued that such quantum spectroscopy signals can be obtained by a simple averaging of their classical spectroscopy counterparts over the Glauber-Sudarshan quasiprobability distribution of the quantum field; the quantum light thus merely provides a novel gating window for the classical response functions. We show that this argument only applies to the linear response and breaks down in the nonlinear regime. The quantum response carries additional valuable information about response and spontaneous fluctuations of matter that may not be retrieved from the classical response by simple data processing. This is connected to the lack of a nonlinear fluctuation-dissipation relation.

We study two-level systems (2LS) coupled at different points to a one-dimensional waveguide in which one end is open and the other is either open (infinite waveguide) or closed by a mirror (semi-infinite). Upon injection of two photons (corresponding to weak coherent driving), the resonance fluorescence and photon correlations are shaped by the effective qubit transition frequencies and decay rates, which are substantially modified by interference effects. In contrast to the well-known result in an infinite waveguide, photons reflected by a single 2LS coupled to a semi-infinite waveguide are initially bunched, a result that can be simply explained by stimulated emission. As the number of 2LS increases (up to 10 are considered here), rapid oscillations build up in the correlations that persist for a very long time. For instance, when the incoming photons are slightly detuned, the transmitted photons in the infinite waveguide are highly antibunched. On the other hand, upon resonant driving, incoherently reflected photons are mostly distributed within the photonic band gap and several sharp side peaks. These features can be explained by considering the poles of the single-particle Green function in the Markovian regime combined with the time delay. Our calculation is not restricted to the Markovian regime, and we obtain several fully non-Markovian results. We show that a single 2LS in a semi-infinite waveguide can not be decoupled by placing it at the node of the photonic field, in contrast to recent results in the Markovian regime. Our results illustrate the complexities that ensue when several qubits are strongly coupled to a bus (the waveguide) as might happen in quantum information processing.

The propagation of light in a resonant atomic vapor can a priori be thought of as a multiple scattering process, in which each scattering event redistributes both the direction and the frequency of the photons. Particularly, the frequency redistribution may result in Lévy flights of photons, directly affecting the transport properties of light in a resonant atomic vapor and turning this propagation into a superdiffusion process. Here, we report on a Monte Carlo simulation developed to study the evolution of the spectrum of the light in a resonant thermal vapor. We observe the gradual change of the spectrum and its convergence towards a regime of complete frequency redistribution as the number of scattering events increases. We also analyze the probability density function of the step length of photons between emissions and reabsorptions in the vapor, which governs the statistics of the light diffusion. We observe two different regimes in the light transport: superdiffusion when the vapor is excited near the line center and normal diffusion for excitation far from the line center. The regime of complete frequency redistribution is not reached for excitation far from resonance even after many absorption and reemission cycles due to correlations between emitted and absorbed frequencies.

We study the propagation of guided light along an array of three-level atoms in the vicinity of an optical nanofiber under the condition of electromagnetically induced transparency. We examine two schemes of atomic levels and field polarizations where the guided probe field is quasilinearly polarized along the major or minor principal axis, which is parallel or perpendicular, respectively, to the radial direction of the atomic position. Our numerical calculations indicate that 200 cesium atoms in a linear array with a length of 100 $\mu \mathrm{m}$ at a distance of 200 nm from the surface of a nanofiber with a radius of 250 nm can slow down the speed of guided probe light by a factor of about $3.5\times {10}^6$ (the corresponding group delay is about 1.17 $\mu \mathrm{s})$. In the neighborhood of the Bragg resonance, a significant fraction of the guided probe light can be reflected back with a negative group delay. The reflectivity and the group delay of the reflected field do not depend on the propagation direction of the probe field. However, when the input guided light is quasilinearly polarized along the major principal axis, the transmittivity and the group delay of the transmitted field substantially depend on the propagation direction of the probe field. Under the Bragg resonance condition, an array of atoms prepared in an appropriate internal state can transmit guided light polarized along the major principal in one specific direction even in the limit of infinitely large atom numbers. The directionality of transmission of guided light through the array of atoms is a consequence of the existence of a longitudinal component of the guided light field as well as the ellipticity of both the field polarization and the atomic dipole vector.