Restrictions on quantum operations give rise to resource theories. Total lack of a shared reference frame for transformations associated with a group $G$ between two parties is equivalent to having, in effect, an invariant channel between the parties and a corresponding superselection rule. The resource associated with the absence of the reference frame is known as “frameness” or “asymmetry.” We show that any entanglement monotone for pure bipartite states can be adapted as a pure-state frameness monotone for phase-invariant channels [equivalently U(1) superselection rules] and extended to the case of mixed states via the convex-roof extension. As an application, we construct a family of concurrence monotones for U(1) frameness for general finite-dimensional Hilbert spaces. Furthermore, we study “frameness of formation” for mixed states analogous to entanglement of formation. In the case of a qubit, we show that it can be expressed as an analytical function of the concurrence analogously to the Wootters formula for entanglement of formation. Our results highlight deep links between entanglement and frameness resource theories.

Pure rotational spectra of the ground electronic-vibrational $X_1$ state of ${}^{204}$Pb${}^{19}$F, ${}^{206}$Pb${}^{19}$F, ${}^{207}$Pb${}^{19}$F, and ${}^{208}$Pb${}^{19}$F are measured with a resonator pulsed supersonic jet Fourier-transform microwave spectrometer. Also reported is a new measurement of the Stark effect on the optical spectra of $A\leftarrow X_1$ transitions. These spectra are combined with published high-resolution infrared spectra of $X_2\leftrightarrow X_1$ transitions in order to create a complete picture of the ground state of lead monofluoride. For the microwave data, molecules are prepared by laser ablation of lead target rods and stabilized in a supersonic jet of neon mixed with sulfur hexafluoride. For the optical Stark spectra, a continuous source of molecules is created in a nozzle heated to $1000{}^{\circ }$C. The microwave spectra confirm, improve, and extend previously reported constants that describe the rotational, spin-orbit, and hyperfine interactions of the ground electronic state of the PbF molecule. A discrepancy concerning the sign of the hyperfine constant describing the ${}^{207}$Pb nucleus is discussed. Magnetic-field-dependent microwave spectra are used to characterize the Zeeman interaction in terms of two $g$ factors of the body-fixed electronic wave function. The optical Stark spectra are used to characterize the electric dipole moment of the $X_1$ and $A$ states.

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping, we find the solution for the whole set of ground-state wave functions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wave functions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system, we propose an analytic expression for the many-body wave function of the inhomogeneous system which well describes the ground state at finite, large, and equal interaction strengths, as validated by numerical simulations.

Temporal coherence of individual signal or idler beam, determined by the spectral correlation property of photon pairs, is important for realizing quantum interference among independent sources. Based on spontaneous four-wave mixing in optical fibers, we study the effect of chirp on the temporal coherence property by introducing a different amount of chirp into either the pulsed pump or individual signal (idler) beam. The investigation shows that the pump chirp induces additional frequency correlation into photon pairs; the mutual spectral correlation of photon pairs and the coherence of individual beam can be characterized by measuring the intensity correlation function $g^{\left(2\right)}$ of the individual beam. To improve the coherence degree, the pump chirp should be minimized. Moreover, a Hong-Ou-Mandel–type two-photon interference experiment with the signal beams generated in two different fibers illustrates that the chirp of the individual signal (idler) beam does not change the temporal coherence degree, but affects the temporal mode matching. To achieve high visibility among multiple sources, apart from improving the coherence degree, mode matching should be optimized by managing the chirps of individual beams.

We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 $+$ 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.

We investigate the generation of multicolor quadripartite entangled beams of light with continuous variables via optomechanical coupling in an optical cavity. It is found that the genuine quadripartite entanglement can be achieved among the Stokes and anti-Stokes sidebands of two driven cavity fields. This entanglement still exists for the environment temperature up to about $50\text{K}$. We also show that the obtained genuine quadripartite entanglement actually results from concurrent four-wave-mixing processes in the system, which can, in principle, be generalized to obtain a genuine $2N$-partite entangled state of light from a generic $N$-mode cavity optomechanical system.

We show that off-mass-shell effects arising from the internal structure of the proton provide a new proton polarization mechanism in the Lamb shift, proportional to the lepton mass to the fourth power. This effect is capable of resolving the current puzzle regarding the difference in the proton radius extracted from muonic compared with electronic hydrogen experiments. These off-mass-shell effects could be probed in several other experiments. A significant ambiguity appearing in dispersion relation evaluations of the proton polarizability contribution to the Lamb shift is noted.

The recent conundrum with the proton charge radius inspires reconsideration of the corrections that enter into determinations of the proton size. We study the two-photon proton-structure corrections, with special consideration of the nonpole subtraction term in the dispersion relation and using fits to modern data to evaluate the energy contributions. We find that individual contributions change more than the total and present results with error estimates.

A photonic analog of the Josephson effect is analyzed for a system formed by a partly transparent mechanical membrane dividing an optical cavity into two halves. Photons tunneling between the two subcavities constitute the coherent Jospehson current. The force acting upon the membrane due to the light pressure induces a nonlinearity, which results in a rich dynamical structure. For example, contrary to standard bosonic Josephson systems, we encounter chaos. By means of a mean-field approach, we identify the various regimes and corresponding phase diagram. At the short time scale, chaos is demonstrated to prevent regular self-trapping, while for longer times a dissipation-induced self-trapping effect is possible.

Quantum solutions and classical orbits are discussed for statically screened Wannier-Mott excitons for two closely related potentials: the Stern-Howard potential and a suggested simple focusing one. Bound states and exact “quantized” values of screening are obtained as well. For the suggested potential, the scattering matrix, the Regge poles, and the transmission coefficient are calculated exactly. We argue that the simple potential can be utilized in applications instead of the Stern-Howard potential, which is difficult to handle.

A number of approaches to the problem of defining arrival- and dwell-time probabilities in quantum theory makes use of idealized models of clocks. An interesting question is the extent to which the probabilities obtained in this way are related to standard semiclassical results. In this paper, we explore this question using a reasonably general clock model, solved using path-integral methods. We find that, in the weak-coupling regime, where the energy of the clock is much less than the energy of the particle it is measuring, the probability for the clock pointer can be expressed in terms of the probability current in the case of arrival times, and the dwell-time operator in the case of dwell times, the expected semiclassical results. In the regime of strong system-clock coupling, we find that the arrival-time probability is proportional to the kinetic-energy density, consistent with an earlier model involving a complex potential. We argue that, properly normalized, this may be the generically expected result in this regime. We show that these conclusions are largely independent of the form of the clock Hamiltonian.

We present a scalable uniform technique for the construction of highly conditional multiply-controlled-not quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.

Given an ensemble of mixed qubit states, it is possible to increase the purity of the constituent states using a procedure known as state purification. The reverse operation, which we refer to as dilution, produces a larger ensemble, while reducing the purity level of the systems. In this paper we find asymptotically optimal procedures for purification and dilution of an ensemble of independently and identically distributed mixed qubit states, for some given input and output purities and an asymptotic output rate. Our solution involves using the statistical tool of local asymptotic normality, which recasts the qubit problem in terms of attenuation and amplification of a single-mode displaced Gaussian state. Therefore, to obtain the qubit solutions, we must first solve the analogous problems in the Gaussian setup. We provide full solutions to all of the above for the (global) trace-norm figure of merit.

We study a system of three trapped ions in an anisotropic bidimensional trap. By focusing on the transverse modes of the ions, we show that the mutual ion-ion Coulomb interactions set entanglement of a genuine tripartite nature, to some extent persistent to the thermal nature of the vibronic modes. We tackle this issue by addressing a nonlocality test in the phase space of the ionic system and quantifying the genuine residual tripartite entanglement in the continuous variable state of the transverse modes.

We have studied mutual projectile and target ionization in 1-MeV/amu N${}^{4+}$ and N${}^{5+}+\mathrm{He}$ collisions in kinematically complete experiments by measuring the momenta of the recoil ion and both ejected electrons in coincidence with the charge-changed projectiles. By means of four-particle Dalitz plots, in which multiple differential cross sections are presented as a function of the momenta of all four particles, experimental spectra are compared with theoretical results from various models. The experimental data are qualitatively reproduced by higher-order calculations, where good agreement is achieved for N${}^{5+}+\mathrm{He}$ collisions, while some discrepancies persist for N${}^{4+}+\mathrm{He}$ collisions.

We present a method for determining the depth of an atomic or molecular trap of any type. This method relies on a measurement of the trap loss rate induced by collisions with background gas particles. Given a fixed gas composition, the loss rate uniquely determines the trap depth. Because of the “soft” long-range nature of the van der Waals interaction, these collisions transfer kinetic energy to trapped particles across a broad range of energy scales, from room temperature to the microkelvin energy scale. The resulting loss rate therefore exhibits a significant variation over an enormous range of trap depths, making this technique a powerful diagnostic with a large dynamic range. We present trap depth measurements of a Rb magneto-optical trap using this method and a different technique that relies on measurements of loss rates during optical excitation of colliding atoms to a repulsive molecular state. The main advantage of the method presented here is its large dynamic range and applicability to traps of any type requiring only knowledge of the background gas density and the interaction potential between the trapped and background gas particles.

The pulse duration and carry-envelope phase (CEP) are two important parameters to characterize a few-cycle intense laser. We systematically study asymmetrical ionization of Ar in few-cycle laser fields with different pulse durations (3–7 fs) and laser intensities (${10}^{13}$–${10}^{14}{\mathrm{W}/\mathrm{cm}}^2$) by solving the time-dependent Schrödinger equation. Analyzing the CEP-dependent asymmetry of above-threshold ionization as a function of the photoelectron energy, we find that the qualitative global features of CEP-dependent asymmetry are insensitive to the pulse duration. But the fine structures of the asymmetry are sensitive to the laser pulse duration. Changing Ar to H atoms, we find that the information encoded in asymmetry is insensitive to target atoms at a moderate laser intensity.

We theoretically analyze a Mach-Zehnder interferometer with trapped condensates and find that it is surprisingly stable against the nonlinearity induced by interparticle interactions. The phase sensitivity, which we study for number-squeezed input states, can overcome the shot noise limit and be increased up to the Heisenberg limit provided that a Bayesian or maximum-likelihood phase estimation strategy is used. We finally demonstrate the robustness of the Mach-Zehnder interferometer in the presence of interactions against condensate oscillations and a realistic atom-counting error.

We investigate quantum phase transitions occurring in a system of strongly interacting ultracold bosons in a one-dimensional optical lattice. After discussing the commensurate-incommensurate transition, we focus on the phases appearing at an incommensurate filling. We find a rich phase diagram, with superfluid, supersolid, and solid (kink-lattice) phases. Supersolids generally appear in theoretical studies of systems with long-range interactions; our results break this paradigm and show that they may also emerge in models including only short-range (contact) interactions, provided that quantum fluctuations are properly taken into account.

We present a method for transferring bosonic atoms residing on the lowest $s$ band of an optical lattice to the first excited $p$ bands. Our idea hinges on resonant tunneling between adjacent sites of accelerated lattices. The acceleration effectively shifts the quasibound energies on each site such that the system can be cast into a Wannier-Stark ladder problem. By adjusting the acceleration constant, a situation of resonant tunneling between the $s$ and $p$ bands is achievable. Within a mean-field model, considering ${}^{87}$Rb atoms, we demonstrate population transfer from the $s$ to the $p$ bands with around 95$\%$ efficiency. Nonlinear effects deriving from atom-atom interactions, as well as coupling of the quasibound Wannier-Stark states to the energy continuum, are considered.