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The interplay of three light-matter interaction processes - rotating and counter-rotating interactions and two-photon relaxation of the light field - is a topic of interest in quantum optics and quantum information processing. In this work, we theoretically investigate the three light-matter interaction processes using the anisotropic Rabi model, which accounts for different strengths of rotating and counter-rotating interactions and the unique occurrence of photon escape exclusively in pairs. By numerically solving the Lindblad master equation, we analyze the excitation-relaxation dynamics and derive a non-Hermitian effective Hamiltonian to gain further physical insights. To explore the individual effects of these interactions, we examine three analytically tractable limits of the effective Hamiltonian. Our analysis reveals that the three competitive light-matter interaction processes exhibit sensitivity to parity, leading to intriguing phenomena in both transient and steady states. Particularly interesting dynamical patterns resembling quantum phase transitions emerge when these three interaction terms compete. This work deepens the understanding of ultrastrong light-matter interaction in open quantum systems and offers valuable insights into cavity-based quantum computations., Comment: 13 pages, 8 figures

In this study, ultrafast optical spectroscopy was employed to elucidate the intricate topological features of EuIn$_2$As$_2$, a promising candidate for a magnetic topological-crystalline axion insulator. Our investigation, focusing on the real-time evolution of topological states, unveiled a narrow surface magnetic gap (2$\Delta_0$ $\simeq$ 8.2 meV)) emerging at the antiferromagnetic transition temperature ($T_N$ $\approx$ 16 K). Below $T_N$, two extremely low-energy collective modes, $\omega_1$ and $\omega_2$, with frequencies of $\sim$9.9 and 21.6 GHz at $T$ = 4 K, respectively, were observed, exhibiting strong temperature dependence. $\omega_1$ correlates with an acoustic phonon, while $\omega_2$ is associated with a magnon. The results suggest that EuIn$_2$As$_2$ has the potential to manifest a magnetic topological-crystalline axion insulator, presenting a small magnetic energy gap on the (001) surface. The findings further our understanding of the interplay between magnetism and topology in this material, showcasing its potential for applications in quantum information processing and spintronics., Comment: 6 pages, 4 figures

We perform a combined analytical and numerical investigation to explore how an analytically designed pulse can precisely control the rotational motions of a single-molecular polariton formed by the strong coupling of two low-lying rotational states with a single-mode cavity. To this end, we derive a pulse-area theorem that gives amplitude and phase conditions of the pulses in the frequency domain for driving the polariton from a given initial state to an arbitrary coherent state. The pulse-area theorem is examined for generating the maximum degree of orientation using a pair of pulses. We show that the phase condition can be satisfied by setting the initial phases of the two identically overlapped pulses or by controlling the time delay between pulses for practical applications., Comment: 6 figures

We present a combined analytical and numerical study for coherent terahertz control of a single molecular polariton, formed by strongly coupling two rotational states of a molecule with a single-mode cavity. Compared to the bare molecules driven by a single terahertz pulse, the presence of a cavity strongly modifies the post-pulse orientation of the polariton, making it difficult to obtain its maximal degree of orientation. To solve this challenging problem toward achieving complete quantum coherent control, we derive an analytical solution of a pulse-driven quantum Jaynes-Cummings model by expanding the wave function into entangled states and constructing an effective Hamiltonian. We utilize it to design a composite terahertz pulse and obtain the maximum degree of orientation of the polariton by exploiting photon blockade effects. This work offers a new strategy to study rotational dynamics in the strong-coupling regime and provides a method for complete quantum coherent control of a single molecular polariton. It, therefore, has direct applications in polariton chemistry and molecular polaritonics for exploring novel quantum optical phenomena., Comment: 16 pages, 5 figures , accepted by Physical Review Letters on 19 December, 2022

According to the Heisenberg uncertainty principle between time and energy fluctuation, a concept of the quantum speed limit (QSL) has been established to determine the minimum evolutionary time between quantum states. Considerable theoretical and experimental efforts are invested in obtaining the QSL time bounds in various scenarios. However, it remains a long-standing goal to derive a meaningful QSL bound for a general quantum problem. Here, we propose a geometrical approach to derive a QSL bound for closed and open quantum systems. By solving a quantum brachistochrone problem in the framework of the Riemannian metric, we show that the QSL between a given initial state to a final state is determined not only by the entire dynamics of the system but also by the individual dynamics of a critical parameter. We exemplify the utility of the new bound in three representative scenarios, demonstrating a pronounced advantage in finding a tight and meaningful QSL bound of a general quantum evolution problem., Comment: 10 pages,4 figures

We derive a pulse-area theorem for a cyclic three-level system, an archetypal model for exploring enantioselective state transfer (ESST) in chiral molecules driven by three linearly polarized microwave pulses. By dividing the closed-loop excitation into two separate stages, we obtain both amplitude and phase conditions of three control fields to generate high fidelity of ESST. As a proof of principle, we apply this pulse-area theorem to the cyclohexylmethanol molecules ($\text{C}_{7}\text{H}_{14}\text{O}$), for which three rotational states are connected by the $a$-type, $b$-type, and $c$-type components of the transition dipole moments in both center-frequency resonant and detuned conditions. Our results show that two enantiomers with opposite handedness can be transferred to different target states by designing three microwave pulses that satisfy the amplitude and phase conditions at the transition frequencies. The corresponding control schemes are robust against the time delays between the two stages. We suggest that the two control fields used in the second stage should be applied simultaneously for practical applications. This work contributes an alternative pulse-area theorem to the field of quantum control, which has the potential to determine the chirality of enantiomers in a mixture., Comment: 21 pages and 7 figures

We present a combined analytical and numerical investigation to show how an optimal control field can be designed to generate maximum field-free orientation of molecules for three populated rotational states. Based on a model involving pure rotational ladder-climbing excitation between rotational states, a set of optimal amplitude and phase conditions are analytically derived for the applied control fields. The maximum degree of orientation can be achieved when the field satisfies amplitude and phase conditions at the two transition frequencies. Multiple optimal solutions exist and to examine these conditions, we devise a quantum coherent control scheme using two terahertz pulses and successfully apply it to the linear polar molecule HCN at ultracold temperature. The sensitivity of both populations and phases of rotational states to control field parameters, i.e., the detuning, bandwidth, and time delay, is analyzed for understanding the optimal orientation mechanism. This work thus examines the frequency domain landscape belonging to optimal pulses., Comment: 21 pages and 10 figures

The phenomenon of quantum revivals resulting from the self-interference of wave packets has been observed in several quantum systems and utilized widely in spectroscopic applications. Here, we present a combined analytical and numerical study on the generation of orientational quantum revivals (OQRs) exclusively using a single-cycle THz pulse. As a proof of principle, we examine the scheme in the linear polar molecule HCN with experimentally accessible pulse parameters and obtain strong field-free OQR without requiring the condition of the sudden-impact limit. To visualize the involved quantum mechanism, we derive a three-state model using the Magnus expansion of the time-evolution operator. Interestingly, the THz pulse interaction with the electric-dipole moment can activate direct multiphoton processes, leading to OQR enhancements beyond that induced by a rotational ladder-climbing mechanism from the rotational ground state. This work provides an explicit and feasible approach toward quantum control of molecular rotation, which is at the core of current research endeavors with potential applications in atomic and molecular physics, photochemistry, and quantum information science., Comment: 17 pages, 6 Figures

We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility of a set of linear matrix inequalities. Thus, it can be efficiently solved using existent numerical solvers. We apply this method to the identification of bound entangled Gaussian states. We show that the proposed method can be used to identify bound entangled Gaussian states that could be simple enough to be producible in quantum optics., Comment: 14 pages

We investigate two classes of quantum control problems by using frequency-domain optimization algorithms in the context of ultrafast laser control of quantum systems. In the first class, the system model is known and a frequency-domain gradient-based optimization algorithm is applied to searching for an optimal control field to selectively and robustly manipulate the population transfer in atomic Rubidium. The other class of quantum control problems involves an experimental system with an unknown model. In the case, we introduce a differential evolution algorithm with a mixed strategy to search for optimal control fields and demonstrate the capability in an ultrafast laser control experiment for the fragmentation of Pr(hfac)$_3$ molecules., Comment: 11 pages, 11 figures

Exploring molecular breakup processes induced by light-matter interactions has both fundamental and practical implications. However, it remains a challenge to elucidate the underlying reaction mechanism in the strong field regime, where the potentials of the reactant are modified dramatically. Here, we perform a theoretical analysis combined with a time-dependent wavepacket calculation to show how a strong ultrafast laser field affects the photofragment products. As an example, we examine the photochemical reaction of breaking up the molecule NaI into the neutral atoms Na and I, which due to inherent nonadiabatic couplings is indirectly formed in a stepwise fashion via the reaction intermediate NaI. By analyzing the angular dependencies of fragment distributions, we are able to identify the reaction intermediate NaI from the weak to the strong field-induced nonadiabatic regimes. Furthermore, the energy levels of NaI can be extracted from the quantum interference patterns of the transient photofragment momentum distribution., Comment: 17 pages, 5 figures

Achieving high-fidelity control of quantum systems is of fundamental importance in physics, chemistry and quantum information sciences. However, the successful implementation of a high-fidelity quantum control scheme also requires robustness against control field fluctuations. Here, we demonstrate a robust optimization method for control of quantum systems by optimizing the spectral phase of an ultrafast laser pulse, which is accomplished in the framework of frequency domain quantum optimal control theory. By incorporating a filtering function of frequency into the optimization algorithm, our numerical simulations in an abstract two-level quantum system as well as in a three-level atomic rubidium show that the optimization procedure can be enforced to search optimal solutions while achieving remarkable robustness against the control field fluctuations, providing an efficient approach to optimize the spectral phase of the ultrafast laser pulse to achieve a desired final quantum state of the system., Comment: 17 pages, 8 figures

The absorption of a single photon that excites a quantum system from a low to a high energy level is an elementary process of light-matter interaction, and a route towards realizing pure single-photon absorption has both fundamental and practical implications in quantum technology. Due to nonlinear optical effects, however, the probability of pure single-photon absorption is usually very low, which is particularly pertinent in the case of strong ultrafast laser pulses with broad bandwidth. Here we demonstrate theoretically a counterintuitive coherent single-photon absorption scheme by eliminating nonlinear interactions of ultrafast laser pulses with quantum systems. That is, a completely linear response of the system with respect to the spectral energy density of the incident light at the transition frequency can be obtained for all transition probabilities between 0 and 100% in a multi-level quantum systems. To that end, a new multi-objective optimization algorithm is developed to find an optimal spectral phase of an ultrafast laser pulse, which is capable of eliminating all possible nonlinear optical responses while maximizing the probability of single-photon absorption between quantum states. This work not only deepens our understanding of light-matter interactions, but also offers a new way to study photophysical and photochemical processes in the "absence" of nonlinear optical effects., Comment: 11 pages, 5 figures