We study the emergence of hysteresis during the process of quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 Bose-Einstein condensate of ultracold atoms. We explicitly demonstrate the appearance of a hysteresis loop with various quench times, showing that it is rate independent for large magnetizations only. In other cases, scaling of the hysteresis loop area is observed, which we explain by using the Kibble-Zurek theory in the limit of small magnetization. The effect of an external harmonic trapping potential is also discussed.

Massless particles, including photons, are not governed by particle conservation law during their typical interaction with matter even at low energies and thus have no chemical potential. However, in driven systems, near-equilibrium dynamics can lead to equilibration of photons with a finite number, describable using an effective chemical potential [M. Hafezi et al., Phys. Rev. B 92, 174305 (2015)]. Here we build upon this general concept with an implementation appropriate for a photon-based quantum simulator. We consider how laser cooling of a well-isolated mechanical mode can provide an effective low-frequency bath for the quantum simulator system. We show that the use of auxiliary photon modes, coupled by the mechanical system, enables control of both the chemical potential and temperature of the resulting photonic quantum simulator's grand canonical ensemble.

Improving the phase resolution of interferometry is crucial for high-precision measurements of various physical quantities. Systematic phase errors dominate the phase uncertainties in most realistic optical interferometers. Here, we propose and experimentally demonstrate a weak measurement scheme to considerably suppress the phase uncertainties by the direct amplification of the phase shift in optical interferometry. Given an initial ultrasmall phase shift between orthogonal polarization states, we observe a phase amplification effect with a factor of 388. Our weak measurement scheme provides a practical approach to significantly improve the interferometric phase resolution, which is favorable for precision measurement applications.

Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that ${\mathcal{T}}^2=-1$ for fermionic systems. In $\mathcal{PT}$-symmetric quantum mechanics an operator has both $\mathcal{PT}$ and $\mathcal{CPT}$ adjoints. Fermionic operators $\eta$, which are quadratically nilpotent (${\eta }^2=0$), and algebras with $\mathcal{PT}$ and $\mathcal{CPT}$ adjoints can be constructed. These algebras obey different anticommutation relations: $\eta {\eta }^{\mathcal{PT}}+{\eta }^{\mathcal{PT}}\eta =-\mathbb{1}$, where ${\eta }^{\mathcal{PT}}$ is the $\mathcal{PT}$ adjoint of $\eta$, and $\eta {\eta }^{\mathcal{CPT}}+{\eta }^{\mathcal{CPT}}\eta =\mathbb{1}$, where ${\eta }^{\mathcal{CPT}}$ is the $\mathcal{CPT}$ adjoint of $\eta$. This paper presents matrix representations for the operator $\eta$ and its $\mathcal{PT}$ and $\mathcal{CPT}$ adjoints in two and four dimensions. A $\mathcal{PT}$-symmetric second-quantized Hamiltonian modeled on quantum electrodynamics that describes a system of interacting fermions and bosons is constructed within this framework and is solved exactly.

We address the trade-off between information and disturbance in qubit thermometry from the perspective of quantum estimation theory. Given a quantum measurement, we quantify information via the Fisher information of the measurement and disturbance via four different figures of merit, which capture different aspects (statistical, thermodynamical, geometrical) of the trade-off. For each disturbance measure, the efficient measurements, i.e., the measurements that introduce a disturbance not greater than any other measurement extracting the same amount of information, are determined explicitly. The family of efficient measurements varies with the choice of the disturbance measure. On the other hand, commutativity between the elements of the probability operator-valued measure (POVM) and the equilibrium state of the thermometer is a necessary condition for efficiency with respect to any figure of disturbance.

We present a general framework for the information backflow (IB) approach of Markovianity that not only includes a large number, if not all, of IB prescriptions proposed so far but also is equivalent to completely positive divisibility for invertible evolutions. Following the common approach of IB, where monotonic decay of some physical property or some information quantifier is seen as the definition of Markovianity, we propose in our framework a general description of what should be called a proper “physicality quantifier” to define Markovianity. We elucidate different properties of our framework and use them to argue that an infinite family of non-Markovianity measures can be constructed, which would capture varied strengths of non-Markovianity in the dynamics. Moreover, we show that generalized trace-distance measure in two dimensions serve as a sufficient criteria for IB Markovianity for a number of prescriptions suggested earlier in the literature.

We introduce several families of quantum fingerprinting protocols to evaluate the equality function on two $n$-bit strings in the simultaneous message passing model. The original quantum fingerprinting protocol uses a tensor product of a small number of $O(logn)$-qubit high-dimensional signals [H. Buhrman et al., Phys. Rev. Lett. 87, 167902 (2001)], whereas a recently proposed optical protocol uses a tensor product of $O\left(n\right)$ single-qubit signals, while maintaining the $O(logn)$ information leakage of the original protocol [J. M. Arazola and N. Lütkenhaus, Phys. Rev. A 89, 062305 (2014)]. We find a family of protocols which interpolate between the original and optical protocols while maintaining the $O(logn)$ information leakage, thus demonstrating a tradeoff between the number of signals sent and the dimension of each signal. There has been interest in experimental realization of the recently proposed optical protocol using coherent states [F. Xu et al., Nat. Commun. 6, 8735 (2015); J.-Y. Guan et al., Phys. Rev. Lett. 116, 240502 (2016)], but as the required number of laser pulses grows linearly with the input size $n$, eventual challenges for the long-time stability of experimental setups arise. We find a coherent state protocol which reduces the number of signals by a factor $\frac{1}{2}$ while also reducing the information leakage. Our reduction makes use of a simple modulation scheme in optical phase space, and we find that more complex modulation schemes are not advantageous. Using a similar technique, we improve a recently proposed coherent state protocol for evaluating the Euclidean distance between two real unit vectors [N. Kumar et al., Phys. Rev. A 95, 032337 (2017)] by reducing the number of signals by a factor $\frac{1}{2}$ and also reducing the information leakage.

We consider state transfer between two qubits—effective two-level systems represented by Rydberg atoms—via a common mode of a microwave cavity at finite temperature. We find that when both qubits have the same coupling strength to the cavity field, at large enough detuning from the cavity mode frequency, quantum interference between the transition paths makes the swap of the excitation between the qubits largely insensitive to the number of thermal photons in the cavity. When, however, the coupling strengths are different, the photon-number-dependent differential Stark shift of the transition frequencies precludes efficient transfer. Nevertheless, using an auxiliary cooling system to continuously extract the cavity photons, we can still achieve a high-fidelity state transfer between the qubits.

The asymmetry of quantum states is an important resource in quantum information processing tasks such as quantum metrology and quantum communication. In this paper, we introduce the notion of asymmetry weight—an operationally motivated asymmetry quantifier in the resource theory of asymmetry. We study the convexity and monotonicity properties of asymmetry weight and focus on its interplay with the corresponding semidefinite programming (SDP) forms along with its connection to other asymmetry measures. Since the SDP form of asymmetry weight is closely related to asymmetry witnesses, we find that the asymmetry weight can be regarded as a (state-dependent) asymmetry witness. Moreover, some specific entanglement witnesses can be viewed as a special case of an asymmetry witness—which indicates a potential connection between asymmetry and entanglement. We also provide an operationally meaningful coherence measure, which we term coherence weight, and investigate its relationship to other coherence measures like the robustness of coherence and the $l_1$ norm of coherence. In particular, we show that for Werner states in any dimension $d$ all three coherence quantifiers, namely, the coherence weight, the robustness of coherence, and the $l_1$ norm of coherence, are equal and are given by a single letter formula.

The ultrafine entanglement witness introduced by Shahandeh et al. [Phys. Rev. Lett. 118, 110502 (2017)] can seamlessly and easily improve any standard entanglement witness. In this paper, by combining the constraint and the test operators, we rotate the hyperplane determined by the test operator and further improve the original ultrafine entanglement witness. In particular, we present a series of ultrafine entanglement witnesses that not only can detect entangled states that the original ultrafine entanglement witnesses cannot detect, but also have the merits that the original ultrafine entanglement witnesses have.

Much of our knowledge of molecular geometry and interaction dynamics comes from indirect measurements of the molecular fragments following breakup. This technique—Coulomb-explosion imaging (CEI), i.e., determining the initial molecular configuration of a system from the momenta of the resulting fragments using knowledge of the particle interactions—is one of the fundamental tools of molecular physics. Moreover, CEI has been a staple of molecular studies for decades. Here we show that one often cannot assign a unique initial configuration to the few-body breakup of a polyatomic molecule given the measurement of the resulting fragments' momenta. Specifically, multiple initial configurations can result in identical momenta for a molecule breaking into three or more parts. Further, the nonunique and nonuniform mapping from the initial configuration to the measured momenta also significantly complicates the determination of molecular alignment at the time of breakup.

We set forth the quantum theory of ionic vibrational-level population by means of tunneling ionization of a molecule. Specific calculations are carried out for the ${\mathrm{H}}_2$ molecule. The results are in qualitative agreement with the experimental data [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. Our account for the excited vibrational levels reveals an interplay of two tendencies which contribute to the ionization rate: (i) It decreases due to additional energy absorption needed to populate these states and (ii) it increases together with the Franck-Condon factors which are large for these states. We show that these two tendencies practically compensate each other. The average quantitative disagreement between the theory and experiment amounts to $\sim 30$%. The same disagreement takes place when using the frozen approximation for the description of the nuclei motion. We demonstrated that the light-dressing effect for ${\mathrm{H}}_2$ leads to the dependence of the ionization rate on the angle between the molecule axis and the polarization vector of the radiation.

We study the Loschmidt echo and the dynamical free energy of the Anderson model after a quench of the disorder strength. If the initial state is extended and the eigenstates of the postquench Hamiltonian are strongly localized, we argue that the Loschmidt echo exhibits zeros periodically with the period $2\pi /D$, where $D$ is the width of spectra. At these zeros, the dynamical free energy diverges in a logarithmic way. We present numerical evidence of our argument in one- and three-dimensional Anderson models. Our findings connect the dynamical quantum phase transitions to the localization-delocalization phase transitions.

As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which corresponds to the Berry curvature measuring the emergent gauge field in momentum space. Here, we first derive the Ginzburg-Landau theory near the critical superfluid transition temperature and then identify and analyze the geometric effects on the effective mass tensor of the Cooper pairs. By showing that the quantum-metric contribution accounts for a sizable fraction of the pair mass in a surprisingly large parameter regime throughout the BCS–Bose-Einstein condensate crossover, we not only reveal the physical origin of its governing role in the superfluid density tensor but also hint at its plausible roles in many other observables.

In this paper, we study the dynamics of the Bose-Hubbard model by using time-dependent Gutzwiller methods. In particular, we vary the parameters in the Hamiltonian as a function of time, and investigate the temporal behavior of the system from the Mott insulator to the superfluid (SF) crossing a second-order phase transition. We first solve a time-dependent Schrödinger equation for the experimental setup recently done by Braun et al. [Proc. Natl. Acad. Sci. USA 112, 3641 (2015)] and show that the numerical and experimental results are in fairly good agreement. However, these results disagree with the Kibble-Zurek scaling. From our numerical study, we reveal a possible source of the discrepancy. Next, we calculate the critical exponents of the correlation length and vortex density in addition to the SF order parameter for a Kibble-Zurek protocol. We show that beside the “freeze” time $\widehat{t}$, there exists another important time, $t_{\mathrm{eq}}$, at which an oscillating behavior of the SF amplitude starts. From calculations of the exponents of the correlation length and vortex density with respect to a quench time ${\tau }_{\mathrm{Q}}$, we obtain a physical picture of a coarsening process. Finally, we study how the system evolves after the quench. We give a global picture of dynamics of the Bose-Hubbard model.

Semiconductor lasers subjected to optical feedback have been intensively used as archetypical testbeds for high-speed (sub-ns) and high-dimensional nonlinear dynamics. By simultaneously extracting all the dynamical variables, we demonstrate that for larger current, the commonly named “quasiperiodic” route is in fact based on mixed external-cavity solutions that lock the oscillation frequency of the intensity, voltage, and separation in optical frequency through a mechanism involving successive rejections along the unstable manifold of an antimode. We show that chaos emerges from a crisis resulting from the inability to maintain locking as the unstable manifold becomes inaccessible.

We report on the observation of a multipeak structure in the correlated two-electron energy distribution from strong-field double ionization of helium using laser pulses with a wavelength of 394 nm and an intensity of $3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. For selected regions of electron emission angles the peaks emerging at energies corresponding to an odd number of absorbed photons are suppressed. We interpret this as direct results of quantum-mechanical selection rules. For neon these features occur for even photon numbers. By that we attribute this effect to the parity of the continuum wave function. A comparison with analogous data for single-photon double ionization is given.

Open quantum dynamics in a tripartite scenario including a system, its environment, and a passive reference is shown to resolve several open questions regarding not completely positive (NCP) dynamical maps as valid descriptions of open quantum evolution. The steering states of the system and the environment with respect to the reference, reduced down to a dense, compact set of states of the system alone, provide a well-defined domain of action for a bonafide dynamical map describing the open evolution of the system. The map is not restricted to being completely positive but it preserves the positivity of all states in its domain. NCP open dynamics corresponding to different initial configurations of the tripartite system are explored.

A quantum money scheme enables a trusted bank to provide untrusted users with verifiable quantum banknotes that cannot be forged. In this work, we report a proof-of-principle experimental demonstration of the preparation and verification of unforgeable quantum banknotes. We employ a security analysis that takes experimental imperfections fully into account. We measure a total of $3.6\times {10}^6$ states in one verification round, limiting the forging probability to ${10}^{-7}$ based on the security analysis. Our results demonstrate the feasibility of preparing and verifying quantum banknotes using currently available experimental techniques.