Multilevel Quantum Systems Research Articles

Selective ultrafast control of multi-level quantum systems by subcycle and unipolar pulses.

The most typical way to optically control population of atomic and molecular systems is to illuminate them with radiation, resonant to the relevant transitions. Here we consider a possibility to control populations with the subcycle and even unipolar pulses, containing less than one oscillation of electric field. Despite the spectrum of such pulses covers several levels at once, we show that it is possible to selectively excite the levels of our choice by varying the driving pulse shape, duration or time delay between consecutive pulses. The pulses which are not unipolar, but have a peak of electric field of one polarity much higher (and shorter) than of the opposite one, are also capable for such control.

The Bayesian inversion problem for thermal average sampling of quantum systems

In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test observables. The method is based on the Bayesian inversion framework, which provides a platform for analyzing the posterior distribution and naturally leads to an efficient numerical sampling algorithm. We highlight that, the stability estimate is obtained by treating the potential functions as intermediate variables in the following way: the discrepancy between two sets of observation data of training observables can bound the distance between corresponding posterior distributions of potential functions, while the latter naturally leads to a bound of the discrepancies between corresponding thermal averages of test observables. Besides, the training observables can be more flexible than finite samples of the local density function, which are mostly used in previous researches. The method also applies to the multi-level quantum systems in the non-adiabatic regime. In addition, we provide extensive numerical tests to verify the accuracy and efficiency of the proposed algorithm.

Vanishing and Revival of Resonance Raman Scattering.

The possibility to manipulate quantum coherence and interference, apart from its fundamental interest in quantum mechanics, is essential for controlling nonlinear optical processes such as high harmonic generation, multiphoton absorption, and stimulated Raman scattering. We show, analytically and numerically, how a nonlinear optical process via resonance Raman scattering (RRS) can be manipulated in a four-level double-Λ system by using pulsed laser fields. We find that two simultaneously excited RRS paths involved in the system can generate an ultimately destructive interference in the broad-bandwidth-limit regime. This, in turn, reduces the four-level system to an equivalent three-level system in a V configuration capable of naturally vanishing RRS effects. We further show that this counterintuitive phenomenon, i.e., the RRS vanishing, can be prevented by transferring a modulated phase of the laser pulse to the system at resonance frequencies. This work demonstrates a clear signature of both quantum destructive and constructive interference by actively controlling resonant multiphoton processes in multilevel quantum systems, and it therefore has potential applications in nonlinear optics, quantum control, and quantum information science.

Speeding up maximum population transfer in periodically driven multi-level quantum systems

A fast and robust approach to controlling the quantum state of a multi-level quantum system is investigated using a twofrequency time-varying potential. A comparison with other related approaches in the context of a two-level system is also presented, showing similar times and fidelities. As a concrete example, we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We show that the transition between the ground and first excited state is about 20 times faster than the one performed using a single frequency, both with fidelity of 99.97%. The transition time is about 3.5 times the minimum allowed by quantum mechanics. A test of the robustness of the approach is presented, concluding that, counter-intuitively, it is not only faster but also easier to tune up two frequencies than one. This robustness makes the approach suitable for real applications.

Erratum: Computable form of the Born-Markov master equation for open multilevel quantum systems [Phys. Rev. A 99 , 022118 (2019)

Erratum: Computable form of the Born-Markov master equation for open multilevel quantum systems [Phys. Rev. A <b>99</b> , 022118 (2019)

Simultaneous sorting many quDits using different input ports

Quantum sorter has gained a lot of attention during the last years due to its wide application in quantum information processing and quantum technologies. A challenging task is the construction of a quantum sorter, which collect many high-dimensional quantum systems, which are simultaneously incident on different input ports of the device. In this paper we give the definition of the general quantum sorter of multi-level quantum systems. We prove the impossibility of the construction of the perfect quantum sorter, which works for many particles incident on any input port, while keeping their states unmodified. Further we propose an approximate multi-particle multi-input-port quantum sorter, which performs the selection of the particles in a certain output port according to the properties of the initial states, but changing the final states. This method is useful for those situations which require high speed of quantum state sorting. Thus, the information contained in the initial states of the particles is revealed by the click statistics of the detectors situated in each output port.

Deterministic quantum state transfer of atoms in a random magnetic field

We propose a method for transferring atoms to a target quantum state for a multilevel quantum system with sequentially increasing, but otherwise unknown, energy splitting. This is achieved with a feedback algorithm that processes off-resonant optical measurements of state populations during adiabatic rapid passage in real-time. Specifically, we reliably perform the transfer $|F=2,m_F=2\rangle \rightarrow |1,1\rangle \rightarrow |2,1\rangle$ for a sample of ultracold $^{87}$Rb in the presence of a random external magnetic field.

Hybrid quantum-classical simulation of quantum speed limits in open quantum systems

The quantum speed limit (QSL) provides a fundamental upper bound on the speed of quantum evolution, but its evaluation in generic open quantum systems still presents a formidable computational challenge. Herein, we introduce a hybrid quantum-classical method for computing QSL times in multi-level open quantum systems. The method is based on a mixed Wigner–Heisenberg representation of the composite quantum dynamics, in which the open subsystem of interest is treated quantum mechanically and the bath is treated in a classical-like fashion. By solving a set of coupled first-order deterministic differential equations for the quantum and classical degrees of freedom, one can compute the QSL time. To demonstrate the utility of the method, we study the unbiased spin-boson model and provide a detailed analysis of the effect of the subsystem-bath coupling strength and bath temperature on the QSL time. In particular, we find a turnover of the QSL time in the strong coupling regime, which is indicative of a speed-up in the quantum evolution. We also apply the method to the Fenna–Matthews–Olson complex model and identify a potential connection between the QSL time and the efficiency of the excitation energy transfer at different temperatures.

Dynamics of Multi-Level Open Quantum Systems with Initial System-Environment Correlations

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level open quantum system with finite number $$N$$ of quantum eigenstates interacting with arbitrary external deterministic fields and dissipative environment simultaneously. Unlike conventional master equations derived by the projection operator method for the quantum systems of this kind so far, these equations are homogeneous in the reduced statistical operator while, at the same time, taking into account initial correlations between the multi-level system and the environment. Consistent representation of the multi-level system evolution in terms of the $$SU(N)$$ operator algebra facilitates efficient numerical analysis of these equations derived for various physically realistic quantum models.

Computable form of the Born-Markov master equation for open multilevel quantum systems

The Redfield and Lindblad forms of the master equations are obtained under not only the Born and Markov approximations but also the secular approximation. In this paper, we propose a computable form of the master equation for open multilevel quantum systems beyond the secular approximation. The proposed form can retain some dynamical effects that are lost due to use of the secular approximation. Two kinds of open multilevel quantum systems are investigated by using this method, and the results are compared to the ones obtained from the Redfield equation and an exactly numerical path integral approach. It is shown that the results obtained from this computable form match those from the exact numerical path integral approach better than results from the Redfield equation. The normal-diffusion coefficient, momentum-damping coefficient, anomalous-diffusion coefficient, etc. in the master equation are also reevaluated.

Non-Markovian quantum interference in multilevel quantum systems: exact master equation approach

We study the non-Markovian dynamics of multilevel quantum systems coupled with a bosonic dissipative environment. Based on the known exact quantum-state diffusion (QSD) equations, we propose a systematic approach to derive exact time-convolutionless master equations for multilevel quantum systems. Through a combination of analytical and numerical approaches, we extract the non-Markovian dynamics of quantum interference in different time scales. Also, we demonstrate the evolution of quantum interference in a four-level system controlled by an external electromagnetic field. Our findings are extended to few-body quantum networks, with a universal formalism established.

Nonadiabatic Geometric Quantum Computation with Parametrically Tunable Coupling

The nonadiabatic geometric quantum computation is promising as it is robust against certain types of local noises. However, its experimental implementation is challenging due to the need of complex control on multi-level and/or multiple quantum systems. Here, we propose to implement it on a two-dimensional square superconducting qubit lattice. In the construction of our geometric quantum gates, we only use the simplest and experimentally accessible control over the qubit states of the involved quantum systems, without introducing any auxiliary state. Specifically, our scheme is achieved by parametrically tunable all-resonant interaction, which leads to high-fidelity quantum gates. Meanwhile, this simple implementation can be conveniently generalized to a composite scenario, which can further suppress the systematic error during the gate operations. In addition, universal nonadiabatic geometric quantum gates in decoherence-free subspace can also be realized based on the tunable coupling between only two transmon qubits, without consulting to multiple qubits and only using two physical qubits to encode a logical qubit. Therefore, our proposal provides a promising way of high-fidelity geometric manipulation for robust solid-state quantum computation.

Nonadiabatic holonomic quantum computation on coupled transmons with ancillaries

The physical implementation of holonomic quantum computation is challenging due to the needed complex controllable interactions in multilevel quantum systems. Here we propose to implement nonadiabatic holonomic quantum computation with conventional capacitive coupled superconducting transmon qubits. A universal set of holonomic gates is constructed with the help of the interaction with an auxiliary qubit rather than relying on delicate control over an auxiliary level of multilevel quantum systems. Explicitly, these quantum gates are realized by tunable interactions in an all-resonant way, which leads to high-fidelity gate operations. In this way, the distinct merit of our scheme is that we use only the lowest two levels of a transmon to form the qubit states. In addition, the auxiliary qubits are in their ground states before and after every gate operation, so that the holonomic gates can be constructed successively. Therefore, our scheme provides a promising method towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.

Generation of high-fidelity quantum control methods for multilevel systems

In recent decades there has been a rapid development of methods to experimentally control individual quantum systems. A broad range of quantum control methods has been developed for two-level systems; however, the complexity of multilevel quantum systems make the development of analogous control methods extremely challenging. Here we exploit the equivalence between multilevel systems with SU(2) symmetry and spin-1/2 systems to develop a technique for generating new robust, high-fidelity, multilevel control methods. As a demonstration of this technique, we develop adiabatic and composite multilevel quantum control methods and experimentally realize these methods using a $^{171}\mathrm{Yb}^{+}$ ion system. We measure the average infidelity of the process in both cases to be around ${10}^{\ensuremath{-}4}$, demonstrating that this technique can be used to develop high-fidelity multilevel quantum control methods and can, for example, be applied to a wide range of quantum computing protocols, including implementations below the fault-tolerant threshold in trapped ions.

Ultrafast Mapping of Coherent Dynamics and Density Matrix Reconstruction in a Terahertz-Assisted Laser Field.

A time-resolved spectroscopic protocol exploiting terahertz-assisted photoionization is proposed to reconstruct transient density matrix. Population and coherence elements are effectively mapped onto spectrally separated peaks in photoionization spectra. The beatings of coherence dynamics can be temporally resolved beyond the pulse duration, and the relative phase between involved states is directly readable from the oscillatory spectral distribution. As demonstrated by a photoexcited multilevel open quantum system, the method shows potential applications for subfemtosecond time-resolved measurements of coherent dynamics with free electron lasers and tabletop laser fields.

Local sensing with the multilevel ac Stark effect

Analyzing weak microwave signals in the GHz regime is a challenging task if the signal level is very low and the photon energy widely undefined. A superconducting qubit can detect signals in the low photon regime, but due to its discrete level structure, it is only sensitive to photons of certain energies. With a multi-level quantum system (qudit) in contrast, the unknown signal frequency and amplitude can be deduced from the higher level AC Stark shift. The measurement accuracy is given by the signal amplitude, its detuning from the discrete qudit energy level structure and the anharmonicity. We demonstrate an energy sensitivity in the order of $10^{-3}$ with a measurement range of more than $1\,\mathrm{GHz}$. Here, using a transmon qubit, we experimentally observe shifts in the transition frequencies involving up to three excited levels. These shifts are in good agreement with an analytic circuit model and master equation simulations. For large detunings, we find the shifts to scale linearly with the power of the applied microwave drive. Exploiting the effect, we demonstrated a power meter which makes it possible to characterize the microwave transmission from source to sample.

Reduced density matrix identification of open quantum system

Identification of performance parameter of a multi-level open quantum system is a central problem in a growing number of applications of information engineering. Based on the quantum tomography, this paper aims at finding a method for identifying reduced density matrix of open quantum system. State identification of open quantum system approaches is presented for two-level, three-level and N-level systems, respectively. The results show that not only the reduced density matrix can be reestablished, but also the quantum state information can be received in quantum tomography experiment.

Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping.

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

Algebraic Aspects of the Dynamics of Quantum Multilevel Systems in the Projection Operator Technique

Using the projection operator method, we obtain approximate time-local and time-nonlocal master equations for the reduced statistical operator of a multilevel quantum system with a finite number N of quantum eigenstates coupled simultaneously to arbitrary classical fields and a dissipative environment. We show that the structure of the obtained equations is significantly simplified if the free Hamiltonian dynamics of the multilevel system under the action of external fields and also its Markovian and non-Markovian evolutions due to coupling to the environment are described via the representation of the multilevel system in terms of the SU(N) algebra, which allows realizing effective numerical algorithms for solving the obtained equations when studying real problems in various fields of theoretical and applied physics.

Algebraic aspects of the driven dynamics in the density operator and correlation functions calculation for multi-level open quantum systems

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.