We show that phase transitions in spin-1 Bose gases and stacked triangular Heisenberg antiferromagnets—an example of frustrated magnets with competing interactions—are described by the same Landau-Ginzburg-Wilson Hamiltonian with $\mathrm{O}\left(3\right)\times \mathrm{O}\left(2\right)$ symmetry. In agreement with previous nonperturbative-renormalization-group studies of the three-dimensional $\mathrm{O}\left(3\right)\times \mathrm{O}\left(2\right)$ model, we find that the transition from the normal phase to the superfluid ferromagnetic phase in a spin-1 Bose gas is weakly first order and shows pseudoscaling behavior. The (nonuniversal) pseudoscaling exponent $\nu$ is fully determined by the scattering lengths $a_0$ and $a_2$. We provide estimates of $\nu$ in ${}^{87}\mathrm{Rb},{}^{41}\mathrm{K}$, and ${}^7\mathrm{Li}$ atom gases which can be tested experimentally. We argue that pseudoscaling comes from either a crossover phenomenon due to proximity of the O(6) Wilson-Fisher fixed point $({}^{87}\mathrm{Rb}$ and ${}^{41}\mathrm{K})$ or the existence of two unphysical fixed points (with complex coordinates) which slow down the RG flow $\left({}^7\mathrm{Li}\right)$. These unphysical fixed points are a remnant of the chiral and antichiral fixed points that exist in the $\mathrm{O}\left(N\right)\times \mathrm{O}\left(2\right)$ model when $N$ is larger than $N_c\simeq 5.3$ (the transition being then second order and controlled by the chiral fixed point). Finally, we discuss a $\mathrm{O}\left(2\right)\times \mathrm{O}\left(2\right)$ lattice model and show that our results, even though we find the transition to be first order, are compatible with Monte Carlo simulations yielding an apparent second-order transition.

The theory of composite bosons (cobosons) made of two fermions [C. K. Law, Phys. Rev. A 71, 034306 (2005); M. C. Tichy et al., Phys. Rev. Lett. 109, 260403 (2012)] converges to ordinary structureless bosons in the limit of infinitely strong entanglement between the fermionic constituents. For finite entanglement, the annihilation operator $\widehat{c}$ of a composite boson couples the $N$-coboson Fock state not only to the $(N-1)$-coboson state—as for ordinary bosons—but also to a component which is orthogonal to the Fock-state ladder of cobosons. Coupling with states orthogonal to the Fock ladder arises also in dynamical processes of cobosons. Here, with a Gedanken experiment involving both mode splitting and collective Hong-Ou-Mandel-like interference, we derive the characteristic physical signature of the states orthogonal to the Fock ladder generated in the splitting process. This allows us to extract the microscopic properties of many-fermion wave functions from the collective coboson behavior. We show that consecutive beam-splitter dynamics increases the deviation from the ideal bosonic behavior pattern, which opens up a rigorous approach to the falsification of coboson theory.

Quantum mechanics dictates bounds for the minimal evolution time between predetermined initial and final states. Several of these quantum-speed-limit (QSL) bounds were derived for nonunitary dynamics using different approaches. Here, we perform a systematic analysis of the most common QSL bounds in the damped Jaynes-Cummings model, covering the Markovian and non-Markovian regimes. We show that only one of the analyzed bounds cleaves to the essence of the QSL theory outlined in the pioneer works of Mandelstam and Tamm and of Margolus and Levitin in the context of unitary evolutions. We also show that all QSL bounds analyzed reflect the fact that in our model non-Markovian effects speed up quantum evolution. However, it is not possible to infer Markovian or non-Markovian behavior of the dynamics by analyzing only the QSL bounds.

We find a single parameter family of genuinely entangled three-qubit pure states, called the maximally Bell-inequality violating states (MBV), which exhibit maximum Bell-inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so-called tangle measure. This in turn implies that there holds a complementary relation between the Bell-inequality violation by the reduced bipartite systems and the tangle present in the three-qubit states, not necessarily pure. The MBV states also exhibit maximum Bell-inequality violation by the reduced bipartite systems of the three-qubit pure states with a fixed amount of genuine tripartite correlation quantified by the generalized geometric measure, a genuine entanglement measure of multiparty pure states, and the discord monogamy score, a multipartite quantum correlation measure from information-theoretic paradigm. The aforementioned complementary relation has also been established for three-qubit pure states for the generalized geometric measure and the discord monogamy score, respectively. The complementarity between the Bell-inequality violation by the reduced bipartite systems and the genuine tripartite correlation suggests that the Bell-inequality violation in the reduced two-qubit system comes at the cost of the total tripartite correlation present in the entire system.

Recently, magnetic-field sensors based on an electron spin of a nitrogen vacancy center in diamond have been studied both from an experimental and theoretical point of view. This system provides a nanoscale magnetometer, and it is possible to detect a precession of a single spin. In this paper, we propose a sensor consisting of an electron spin and a nuclear spin in diamond. Although the electron spin has a reasonable interaction strength with magnetic field, the coherence time of the spin is relatively short. On the other hand, the nuclear spin has a longer lifetime while the spin has a negligible interaction with magnetic fields. We show that, through the combination of such two different spins via the hyperfine interaction, it is possible to construct a magnetic-field sensor with the sensitivity far beyond that of previous sensors using just a single electron spin.

Nuclear recoil corrections of order ${\alpha }^6{m}^2/M$ are calculated for the lowest-lying triplet states of the helium atom. It improves the theoretical prediction for the isotope shift of the $2{}^{3}S-2{}^{3}P$ transition energy and influences the determination of the ${}^3\mathrm{He}-{}^4\mathrm{He}$ nuclear charge radii difference. This calculation is a step forward on the way towards the direct determination of the charge radius of the helium nucleus from spectroscopic measurements.

We report a time-resolved electron momentum spectroscopy (TREMS) study on the toluene molecule in its $S_1$ excited state. The toluene $S_1$ state was prepared by a 267-nm pump laser and probed with a train of 1.2-keV incident electron beam pulses, each having 1-ps temporal width. It is shown through comparisons with molecular calculations that TREMS has an inherent capability to observe spatial distributions, in momentum space, of not only the outermost orbital but also all other, more tightly bound orbitals of a molecular excited state.

The directional control of molecular dissociation with a laser electric field waveform is a paradigm and was demonstrated for a variety of molecules. In most cases, the directional control occurs via a dissociative ionization pathway. The role of laser-induced coupling of electronic states in the dissociating ion versus selective ionization of oriented neutral molecules, however, could not be distinguished for even small heteronuclear molecules such as CO. Here, we introduce a technique, using elliptically polarized pump and linearly polarized two-color probe pulses, that unambiguously distinguishes the roles of laser-induced state coupling and selective ionization. The measured photoelectron momentum distributions governed by the light polarizations allow us to coincidentally identify the ionization and dissociation from the pump and probe pulses. Directional dissociation of ${\mathrm{CO}}^{+}$ as a function of the relative phase of the linearly polarized two-color pulse is observed for both parallel and orthogonally oriented molecules. We find that the laser-induced coupling of various electronic states of ${\mathrm{CO}}^{+}$ plays an important role for the observed directional bond breaking, which is verified by quantum calculations.

We consider ultracold atoms inside a ring optical cavity that supports a single plane-wave mode. The cavity field, together with an external coherent laser field, drives a two-photon Raman transition between two internal pseudospin states of the atom. This gives rise to an effective coupling between atom's pseudospin and external center-of-mass (COM) motion. For the case of a single atom inside the cavity, We show how the spin-orbit coupling modifies the static and dynamic properties of the Jaynes-Cummings (JC) model. In the case of many atoms in thermodynamic limit, we show that the spin-orbit coupling modifies the Dicke superradiance phase transition boundary and the non-superradiant normal phase may become reentrant in some regimes.

We employ the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method to study excited states of interacting Bose-Einstein condensates confined by harmonic and double-well trap potentials. Two approaches to access excitations, one static and the other dynamic, are investigated and contrasted. In static simulations the low-lying excitations are computed by utilizing a linear-response theory constructed on top of a static MCTDHB solution (LR-MCTDHB). Complimentarily, we propose two dynamic protocols that address excitations by propagating the MCTDHB wave function. In particular, we investigate dipolelike oscillations induced by shifting the origin of the confining potential and breathinglike excitations by quenching the frequency of a parabolic part of the trap. To contrast static predictions and dynamic results we compute the time evolution and regard the respective Fourier transform of several local and nonlocal observables. Namely, we study the expectation value of the position operator $\langle x\left(t\right)\rangle$, its variance $\mathrm{Var}\left[x\right(t\left)\right]$, and a local density computed at selected positions. We find that the variance is the most sensitive and informative quantity: Along with excitations it contains information about deexcitations even in a linear regime of the induced dynamics. The dynamic protocols are found to access the many-body excitations predicted by the static LR-MCTDHB approach.

Standard weak measurement (SWM) has been proved to be a useful ingredient for measuring small longitudinal phase change (LPC) [X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and Guang-Can Guo, Phys. Rev. Lett. 111, 033604 (2013)]. In these SWM proposals, the working regime is selected where the relative phase between orthogonal components is zero, and the LPC can be detected by measuring the shift of the meter state, i.e., the time and frequency domain, which are conjugated observables. Here, we show that an extra bias phase can significantly improve the sensitivity of measuring LPC. This bias phase can be introduced by a precoupling process. Together with a special postselection, a destructive interference can be observed in both the time and frequency domain. Using a broadband source, this conjugated destructive interference occurs in a regime less than 1 as, while the related spectral shift reaches hundreds of THz, resulting in sensitivity outperforming SWM by two orders of magnitude.

We introduce a general parameter $Q_{\mathrm{PB}}$ that provides an experimentally accessible nonclassicality measure for light. The parameter is quantified by the click statistics obtained from on-off detectors in a general multiplexing detection setup. Sub-Poisson-binomial statistics, observed by $Q_{\mathrm{PB}}<0$, indicates that a given state of light is nonclassical. Our parameter replaces the binomial parameter $Q_{\mathrm{B}}$ for more general cases, where any unbalance among the multiplexed modes is allowed, thus enabling the use of arbitrary multiplexing schemes. The significance of the parameter $Q_{\mathrm{PB}}$ is theoretically examined in a measurement setup that only consists of a ring resonator and a single on-off detector. The proposed setup exploits minimal experimental resources and is geared towards a fully integrated quantum nanophotonic circuit. The results show that nonclassical features remain noticeable even in the presence of significant losses, rendering our nonclassicality test more practical and sufficiently flexible to be used in various nanophotonic platforms.

We present a generalized theory and experimental results of the action signals induced by the absorption of two photons from two phase-modulated laser beams. In our experiment, the phases of the laser beams are modulated at the frequencies ${\varphi }_1$ and ${\varphi }_2$, respectively. Their collinear combination leads to the modulation of the total intensity at the frequency $\varphi =\left|{\varphi }_2-{\varphi }_1\right|$. The action signals, such as photoluminescence and photocurrent, which result from the absorption of two photons, are isolated at frequencies $m\varphi , m\in \{0,1,2,\cdots \}$. We demonstrate that the ratio of the amplitudes of the secondary ($m=2$) and the primary ($m=1$) signals $A_{2\varphi }:A_{\varphi }$ is sensitive to the type of relaxation processes in the media. Such sensitivity originates from the cumulative effects of the nonequilibrated state of the matter between the pulses. When the cumulative effects are small, i.e., the relaxation time is much shorter than the laser repetition rate or the laser intensity is high enough to dominate the system behavior, the ratio achieves the reference value of $1:4$. This ratio decreases monotonically as the relaxation time increases. Our experimental results from fluorescent molecules rhodamine 6G and rubrene support these theoretical findings. In the case of a second-order relaxation process, the ratio changes rapidly with the excitation intensity. When the recombination rate in the second-order process is significantly slower than the repetition rate of the laser, we observe nonmonotonic behavior of the ratio as a function of excitation population at low excitation intensity, and when the recombination rate and the excitation intensity are high, the ratio approaches the value of $1:4$. We also use the model to determine the value of the recombination rate of charge carriers in a GaP photodiode.

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics and paraxial optics.

We consider a composite system consisting of coupled particles, and investigate decoherence due to coupling of the center-of-mass degree of freedom to the internal vibrational degrees of freedom. For a composite system of bound particles, we show that in general such a decoherence effect exists, and leads to suppression of interference between different paths of the center-of-mass. For the special case of harmonically-bound particles moving in an external potential, we show that the coupling between the center-of-mass and internal degrees of freedom takes the form of parametric driving of the vibrational degrees of freedom, and that nontrivial coupling depends on the second derivative of the external potential. We find a solution to this parametric driving problem in one dimension for a fixed center-of-mass trajectory. We also propose a measure of compositeness, which quantifies the extent to which such a composite system cannot be approximated as a single, indivisible particle. We perform numerical simulations for a simple interference experiment, consisting of two wave packets scattering off of a square well, and show a close connection between suppression of interference and entanglement between the center-of-mass and internal degrees of freedom, which depends on the initial state of the internal mode. We also calculate the measure of compositeness for this system.

In quantum information processing, one often considers inserting a barrier into a box containing a particle to generate one bit of Shannon entropy. We formulate this problem as a one-dimensional Schrödinger equation with a time-dependent $\delta \text{-function}$ potential. It is a natural generalization of the particle in a box, a canonical example of quantum mechanics, and we present analytic and numerical investigations on this problem. After deriving an exact Volterra-type integral equation, composed of an infinite sum of modes, we show that approximate formulas with the lowest-frequency modes correctly capture the qualitative behavior of the wave function. If we take into account hundreds of modes, our numerical calculation shows that the quantum adiabatic theorem actually gives a very good approximation even if the barrier height diverges within finite time, as long as it is sufficiently longer than the characteristic time scale of the particle. In particular, if the barrier is slowly inserted at an asymmetric position, the particle is localized by the insertion itself, in accordance with a prediction of the adiabatic theorem. On the other hand, when the barrier is inserted quickly, the wave function becomes rugged after the insertion because of the energy transfer to the particle. Regardless of the position of the barrier, the fast insertion leaves the particle unlocalized so that we can obtain meaningful information by a which-side measurement. Our numerical procedure provides a precise way to calculate the wave function throughout the process, from which one can estimate the amount of this information for an arbitrary insertion protocol.

We propose a systematic procedure to optimize quantum state tomography protocols for continuous variable systems based on excitation counting preceded by a displacement operation. Compared with conventional tomography based on Husimi or Wigner function measurement, the excitation counting approach can significantly reduce the number of measurement settings. We investigate both informational completeness and robustness, and provide a bound of reconstruction error involving the condition number of the sensing map. We also identify the measurement settings that optimize this error bound, and demonstrate that the improved reconstruction robustness can lead to an order-of-magnitude reduction of estimation error with given resources. This optimization procedure is general and can incorporate prior information of the unknown state to further simplify the protocol.

We consider the notion of unitary transformations forming bases for subspaces of $M(d,\mathbb{C})$ such that the square of the Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case, we construct the maximal number of such bases for the four- and two-dimensional subspaces while proving the nonexistence of such a construction for the three-dimensional case. Extending this to higher dimensions, we commit to such a construct for the case of qutrits and provide evidence for the existence of such unitaries for prime dimensional quantum systems. Focusing on the qubit case, we show that the average fidelity for estimating any such transformation is equal to the case for estimating a completely unknown unitary from $\text{SU}\left(2\right)$. This is then followed by a quick application for such unitaries in a quantum cryptographic setup.

We present the convergence study of a recurrence entanglement purification protocol using arbitrary two-qubit initial states. The protocol is based on a rank 2 projector in the Bell basis which serves as a two-qubit operation replacing the usual controlled-not gate. We show that the whole space of two-qubit density matrices is mapped onto an invariant subspace characterized by seven real parameters. By analyzing this type of density matrices we are able to find general conditions for entanglement purification in the form of two inequalities between pairs of diagonal elements and pairs of coherences. We show that purifiable initial states do not necessary require a fidelity larger than one half with respect to any maximally entangled pure state. Furthermore, we find a family of states parametrized by their concurrence that can be perfectly converted into a Bell state in just one step of the protocol with probability proportional to the square of the concurrence.