In the field of continuous variables and particularly of Gaussian states an important role is played by the statistics of photon numbers. This issue has been considered in pioneering works for the one- and two-mode cases, but a systematic approach seems not to be available. In this paper, the most general multimode mixed Gaussian state, which is generated starting from a multimode thermal state and processed by the most general Gaussian unitary, is considered. In the $N$-mode the photon numbers are represented by $N$ random variables, one for each mode, and the target is the evaluation of the means and of the covariances. The means describe statistically the amount of photon numbers in each mode, while the covariances give the correlations between the photon numbers in the different modes. For both means and covariances a closed-form result is obtained, expressed in simple and compact formulas. The main tools are provided by the representation of Gaussian unitaries (given by a cascade of an $N$-mode squeeze operator, an $N$-mode rotation operator, and a parallel set of $N$ single-mode displacement operators) and by the corresponding Bogoliubov transformations.

Quantum entanglement is a key resource that can be exploited for a range of applications such as quantum teleportation, quantum computation, and quantum cryptography. However, efforts to exploit entanglement in imaging systems have so far led to solutions such as ghost imaging, that have since found classical implementations. Here, we demonstrate an optical imaging protocol that relies uniquely on entanglement: Two polarizing patterns imprinted and superimposed on a metasurface are separately imaged only when using entangled photons. Unentangled light is not able to distinguish between the two patterns. Entangled single-photon imaging of functional metasurfaces promises advances towards the use of nanostructured subwavelength thin devices in quantum information protocols and a route to efficient quantum state tomography.

It is widely spread in the literature that non-Markovianity (NM) may be regarded as a resource in quantum mechanics. However, it is still unclear how and when this alleged resource may be exploited. Here, we study the relationship between NM and quantum optimal control under the objective of generating entanglement within $M$ noninteracting subsystems, each one coupled to the same non-Markovian environment. Thus, we design a variety of entangling protocols that are only achievable due to the existence of the environment. We show that NM plays a crucial role in all the entangling protocols considered, revealing that the degree of NM completely determines the success of the entangling operation performed by the control. This is a demonstration of the virtues of NM and the way that it can be exploited in a general entangling setup.

We experimentally emulate, in a controlled fashion, the non-Markovian dynamics of a pure dephasing spin-boson model at zero temperature. Specifically, we use a randomized set of external radio-frequency fields to engineer a desired noise power spectrum to effectively realize a non-Markovian environment for a single NMR qubit. The information backflow, characteristic to the non-Markovianity, is captured in the nonmonotonicity of the decoherence function and von Neumann entropy of the system. Using such emulated non-Markovian environments, we experimentally study the efficiency of the Carr-Purcell-Meiboom-Gill dynamical decoupling (DD) sequence to inhibit the loss of coherence. Using the filter function formalism, we design optimized DD sequences that maximize coherence protection for non-Markovian environments and study their efficiencies experimentally. Finally, we discuss DD-assisted tuning of the effective non-Markovianity.

Resonance (quasinormal) states correspond to non-Hermitian solutions to the Schrödinger equation obeying outgoing boundary conditions which lead to complex energy eigenvalues and momenta. Following the normalization rule for resonance states obtained from the residue at a complex pole of the outgoing Green's function to the problem, we propose a definition of expectation value for these states and use it to investigate the extent of validity of the Heisenberg uncertainty relations for potentials that vanish after a distance. We derive analytical expressions for the expectation values involving the momentum and the position for a given resonance state and find in model calculations that the Heisenberg uncertainty relations are satisfied for a broad range of potential parameters. A comparison of our approach with that based on the regularization method by Zel'dovich yields very similar results except for resonance energies very close to the energy threshold. Our work shows that the validity of the Heisenberg uncertainty relations may be extended to the non-Hermitian resonance-state solutions to the Schrödinger equation.

Certain quantum operations can be built more efficiently through a procedure known as repeat-until-success (RUS). Differently from other nondeterministic quantum operations, this procedure provides a classical flag which certifies the success or failure of the procedure and, in the latter case, a recovery step allows the restoration of the quantum state to its original condition. The procedure can then be repeated until success is achieved. After success is certified, the RUS procedure can be equated to a coherent gate. However, this is not the case when the operation needs to be conditioned on the state of other qubits, possibly being in a superposition state. In this situation, the final operation depends on the failure and success history and introduces a “distortion” that, even after the final success, depends on the past outcomes. We quantify the distortion and show that it can be reduced by increasing the probability of success towards unity. While this can be achieved via oblivious amplitude amplification when the original success probability is known, we propose the use of fixed-point oblivious amplitude amplification to reduce this unwanted distortion below any given threshold even without knowing the initial success probability.

Penning traps, with their ability to control planar crystals of tens to hundreds of ions, are versatile quantum simulators. Thermal occupations of the motional drumhead modes, transverse to the plane of the ion crystal, degrade the quality of quantum simulations. Laser cooling using electromagnetically induced transparency (EIT cooling) is attractive as an efficient way to quickly initialize the drumhead modes to near ground-state occupations. We numerically investigate the efficiency of EIT cooling of planar ion crystals in a Penning trap, accounting for complications arising from the nature of the trap and from the simultaneous cooling of multiple ions. We show that, in spite of challenges, the large bandwidth of drumhead modes (hundreds of kilohertz) can be rapidly cooled to near ground-state occupations within a few hundred microseconds. Our predictions for the center-of-mass mode include a cooling time constant of tens of microseconds and an enhancement of the cooling rate with increasing number of ions. Successful experimental demonstrations of EIT cooling in the NIST Penning trap [Jordan et al., [Phys. Rev. Lett. 122, 053603 (2019)] validate our predictions.

We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov–de Gennes equations both numerically and analytically, we find that the stability problem effectively reduces to that of the standard Gross-Pitaevskii equation, proving that the solitons are stable to linear perturbations. In addition, we formulate the stability problem in the framework of the Vakhitov-Kolokolov criterion and provide supplementary numerical simulations which illustrate the absence of instabilities when the soliton is initially perturbed. These results justify the production of chiral solitons in ultracold experiments and their potential application for practical transport dynamics in interferometry and atomtronics.

Self-accelerating waves in conservative systems, which usually feature slowly decaying tails, such as Airy waves, have drawn great interest in studies of quantum and classical wave dynamics. They typically appear in linear media, while nonlinearities tend to deform and eventually destroy them. We demonstrate, by means of analytical and numerical methods, the existence of robust one- and two-dimensional (1D and 2D) self-accelerating tailless solitons and solitary vortices in a model of two-component Bose-Einstein condensates, dressed by a microwave (MW) field, whose magnetic component mediates long-range interaction between the matter-wave constituents, with the feedback of the matter waves on the MW field taken into account. In particular, self-accelerating 2D solitons may move along a curved trajectory in the coordinate plane. The system may also include the spin-orbit coupling between the components, leading to similar results for the self-acceleration. The effect persists if the contact cubic nonlinearity is included. A similar mechanism may generate 1D and 2D self-accelerating solitons in optical media with thermal nonlinearity.

Mollow physics in the two-photon regime shows interesting features such as versatile generation of highly correlated photon pairs, timely ordered and energy tunable. Here, we calculate analytically the power spectral density $S\left(\omega \right)$ and the two-photon correlations $g^{\left(2\right)}\left(\tau \right)$, which are essential to discuss and study such phenomena in the resonant-driven dressed-state regime. It is shown that there exist upper and lower bounds of the $g^{\left(2\right)}\left(\tau \right)$ function for certain spectrally selected photon pairs. Recently reported experiments agree with the presented theory and thereby it is shown that the resonant-driven four-level system is an interesting source for steerable quantum light in quantum cascade setups. We furthermore discuss the unlikeliness of observing antibunching for the delay time $\tau =0$ in the exciton-biexciton correlation functions in such experiments, since antibunching stems from a coherent and in-phase superposition of different photon-emission events. Due to the occurring laser photon scattering, this coherent superposition state is easily disturbed and leads to correlation functions of $g^{\left(2\right)}\left(0\right)=1$.

Classical resolution criteria such as Rayleigh's and Sparrow's are based on the fringe structure produced by Fresnel diffraction or Fraunhofer diffraction. However, these two diffraction theories are based on the assumption of large-aperture scale and are thus incapable of describing the diffraction of subwavelength structure. We find a singularity near the incident wave vector $k_0$ in a subwavelength aperture by considering Rayleigh-Sommerfeld diffraction. The diffraction fringe structure disappears once the aperture scale is smaller than a threshold value. A two-point resolution criterion unrelated to the fringe structure is proposed based on the second-order derivative of the field structure. Numerical results indicate that, for the illumination wavelength of $\lambda =500\mathrm{nm}$, resolution of two 100-nm rectangular holes under near-field Rayleigh-Sommerfeld diffraction is improved by about 300 and 20% in the $x$ and $z$ directions, respectively, compared with the Sparrow criterion, while the lateral resolution limit is reduced to 35 nm.

Quantum-enhanced phase estimation paves the way for precision measurements and is of great realistic significance. In this paper we theoretically investigate the second-order nonlinear phase estimation using a coherent state and parity measurement. A numerical expression of the parity signal is derived, and its visibility is analyzed. The resolution and sensitivity of the signal are compared to a linear phase estimation protocol with the same input and measurement. Additionally, by using the phase-averaging approach, we make an attempt at unveiling the lowdown on a conclusive sensitivity limit without external phase reference. Finally, the effects of several realistic scenarios on the resolution and sensitivity are studied, including photon loss, imperfect detector, those which are a combination thereof, and unbalanced beam splitter.

Recently, it has been shown that at most two observers (Bobs) can sequentially demonstrate bipartite nonlocality with a spatially separated single observer (Alice) invoking a scenario where an entangled system of two spin-$\frac{1}{2}$ particles are shared between a single Alice in one wing and several Bobs on the other wing, who act sequentially and independently of each other [Phys. Rev. Lett. 114, 250401 (2015)]. This has been probed through the quantum violations of CHSH inequality, i.e., when each observer performs two dichotomic measurements. In the present study we investigate how many Bobs can sequentially demonstrate bipartite nonlocality with a single Alice in the above scenario when the number of measurement settings per observer is increased. It is shown that at most two Bobs can exhibit bipartite nonlocality with a single Alice using local realist inequalities with three as well as four dichotomic measurements per observer. We then conjecture that the above feature remains unchanged contingent upon using local realist inequalities with $n$ dichotomic measurements per observer, where $n$ is arbitrary. We further present the robustness of bipartite nonlocality sharing in the above scenario against the entanglement and mixedness of the shared state.

We study atom losses associated to a previously unreported magnetic Feshbach resonance in ${}^{39}\mathrm{K}$. This resonance is peculiar in that it presents $d$-wave character both in the open and closed channels, directly coupled by the dominant spin-exchange interaction. The losses associated to a $d$-wave open-channel resonance present specific signatures such as strong temperature dependance and anisotropic line shapes. The resonance strength and position depend on the axial projection of the orbital angular momentum of the system and are extracted from rigorous multichannel calculations. A two-step model, with an intermediate collision complex being ejected from the trap after collisions with free atoms, permits us to reproduce the observed dependance of the loss rate as a function of temperature and magnetic field.

We theoretically show how the effective focusing and defocusing of a diverging atomic beam can be realized using an appropriate sequence of linearly chirped few-cycle pulsed laser fields. First, we investigate and show that the time averaged optical dipole force induced by the sequence of either positively or negatively chirped pulses vanishes due to the periodic oscillations of the phases of in-phase components of atomic dipole moments. Then, we demonstrate that this issue could be overcome by utilizing a sequence of alternatively chirped pulses instead of either positively or negatively chirped pulses. It is shown that for such a sequence of pulses, the phases of in-phase components of atomic dipole moments does not oscillate periodically and in fact remain constant at either 0 or $\pi$ depending on the chirping direction of the initial pulse, resulting in either an effective focusing or defocusing optical dipole force. The trajectory of atoms under an optical dipole force is also investigated to actually show the focusing and defocusing. Finally, the role of beam shape on the proposed scheme is investigated and it turns out that a super-Gaussian pulse of order $m=2$ shows more efficacy compared to the normal Gaussian pulse.

Radiation generated by a charge moving in a vacuum channel through a dielectric cone is analyzed. The size of the conical target is assumed to be much greater than the wavelengths under consideration. We calculate the wave field outside the target using Stratton-Chu formulas (“aperture integrals”). This work focuses mainly on investigation of the electromagnetic field in the far-field area (Fraunhofer area). We calculate representative radiation patterns and show that typically the maximal radiation is generated in the direction of one of the refracted rays. However, in the specific case where the refracted ray is parallel to the symmetry axis, the maximal radiation is observed at some small (but nonzero) angle with respect to this axis. The maximum radiation in this case is much more intensive compared to all other situations. This phenomenon can be referred to as the “Cherenkov spotlight.”

We theoretically explore a quantum memory using a single nanoparticle levitated in an optical dipole trap and subjected to feedback cooling. This protocol is realized by storing and retrieving a single-photon quantum state from a mechanical mode in levitated cavityless optomechanics. We describe the effectiveness of the photon-phonon-photon transfer in terms of the fidelity, the Wigner function, and the zero-delay second-order autocorrelation function. For experimentally accessible parameters, our numerical results indicate robust conversion of the quantum states of the input signal photon to those of the retrieved photon. We also show that high fidelity single-photon wavelength conversion is possible in the system as long as intense control pulses shorter than the mechanical damping time are used. Our work opens up the possibility of using levitated optomechanical systems for applications of quantum information processing.

We demonstrate theoretically the existence of optical coherence band gaps by performing simulations of partially coherent light incident on a linear array of circular holes in a subwavelength-thickness gold sheet. We use a simple scalar Foldy-Lax system of equations for our model. A possible physical mechanism for the band gaps is discussed.