Simple Quantum Systems Research Articles

Inverse Mpemba Effect Demonstrated on a Single Trapped Ion Qubit.

The Mpemba effect is a counterintuitive phenomena in which a hot system reaches a cold temperature faster than a colder system, under otherwise identical conditions. Here, we propose a quantum analog of the Mpemba effect, on the simplest quantum system, a qubit. Specifically, we show it exhibits an inverse effect, in which a cold qubit reaches a hot temperature faster than a hot qubit. Furthermore, in our system a cold qubit can heat up exponentially faster, manifesting the strong version of the effect. This occurs only for sufficiently coherent systems, making this effect quantum mechanical, i.e., due to interference effects. We experimentally demonstrate our findings on a single ^{88}Sr^{+} trapped ion qubit. The existence of this anomalous relaxation effect in simple quantum systems reveals its fundamentality, and may have a role in designing and operating quantum information processing devices.

Thermodynamic state convertibility is determined by qubit cooling and heating

Thermodynamics plays an important role both in the foundations of physics and in technological applications. An operational perspective adopted in recent years is to formulate it as a quantum resource theory. At the core of this theory is the interconversion between athermality states, i.e. states out of thermal equilibrium. Here, we solve the question of how athermality can be used to heat and cool other quantum systems that are initially at thermal equilibrium. We then show that the convertibility between quasi-classical resources (resources that do not exhibit coherence between different energy eigenstates) is fully characterized by their ability to cool and heat qubits, i.e. by two of the most fundamental thermodynamical tasks on the simplest quantum systems.

The Vortex Surface in a Three-Body Quantum System

Vortices are structures known in our daily lives and observed in a wide variety of systems, from cosmic to microscopic scales. Relatively recent studies showed that vortices could also appear in simple quantum systems. For instance, they were observed experimentally and theoretically as isolated zeros in the differential cross section in atomic ionization processes by the impact of charged particles. In this work, we show that the appearance of these quantum vortices as point structures was not due to any intrinsic property of them, but to the use of restrictive geometries in their visualization. In particular, we show that by studying the fully differential cross section for hydrogen ionization by positron impact, these vortex points are actually a manifestation of a more complex and hitherto unexplored structure, a 3D “vortex surface”.

Generation of an ultrahigh-repetition-rate optical half-cycle pulse train in the nested quantum wells.

We propose a simple quantum system, namely, a nested quantum-well structure, which is able to generate a train of half-cycle pulses of a few-femtosecond duration when driven by a static electric field. We theoretically investigate the emission of such a structure and its dependence on the parameters of the quantum wells. It is shown that the production of a regular output pulse train with tunable properties and the pulse repetition frequencies of tens of terahertz is possible in certain parameter ranges. We expect the suggested structure can be used as an ultra-compact source of subcycle pulses in the optical range.

A modified Bohr’s quantization rule to estimate the energy levels of relativistic systems

Abstract Estimation of quantum energy levels is crucial to understand the physical systems in both non relativistic and relativistic domains. Here we put forward a new method to deduce quantized energy levels of some simple relativistic quantum systems without solving wave equations but using Bohr’s quantization rule along with a few suitable modifications. The results obtained are in good agreement with formal calculations available in the literature.

Transition in eigenvalue statistics due to tunneling in a simple quantum system.

Statistical properties of the sequence of energy eigenvalues in a quantum system are related to the classical dynamics of the system. Sequences of energy levels for classically regular systems generally exhibit Poisson statistics, while those for classically chaotic systems exhibit random matrix statistics. For many systems the classical dynamics can change from regular to chaotic as the result of changing a system parameter and the quantum system shows a corresponding change in its eigenvalue statistics. Here we present a simple quantum system, composed of an infinite square well with several Dirac delta barriers placed inside it, that exhibits a change in eigenvalue statistics as the transmission probability T through the delta barriers changes. For T≈0 the distribution of level spacings is Poisson-like, but increasing T causes the distribution to change to match that of the Gaussian Orthogonal Ensemble. For even greater T values the level spacing distribution becomes Gaussian with a standard deviation that approaches zero as T→1. A similar transition in statistics is seen in the number variance for the eigenvalue sequence. We also demonstrate that the structure of the energy eigenstates changes from highly localized at T≈0 to evenly spread across the infinite square well as T→1. Our model system can be viewed as an example of a quantum graph, and we show that our results match with the expectations for quantum graphs in the limit T→0.

Ultrastable, high-repetition-rate attosecond beamline for time-resolved XUV–IR coincidence spectroscopy

The implementation of attosecond photoelectron–photoion coincidence spectroscopy for the investigation of atomic and molecular dynamics calls for a high-repetition-rate driving source combined with experimental setups characterized by excellent stability for data acquisition over time intervals ranging from a few hours up to a few days. This requirement is crucial for the investigation of processes characterized by low cross sections and for the characterization of fully differential photoelectron(s) and photoion(s) angular and energy distributions. We demonstrate that the implementation of industrial-grade lasers, combined with a careful design of the delay line implemented in the pump–probe setup, allows one to reach ultrastable experimental conditions leading to an error in the estimation of the time delays of only 12 as over an acquisition time of 6.5 h. This result opens up new possibilities for the investigation of attosecond dynamics in simple quantum systems.

Creation of nonclassical states of light in a chiral waveguide

Creating nonclassical states of light from simple quantum systems together with classical resources is a challenging problem. We show how chiral emitters under a coherent drive can generate nonclassical photon states. For our analysis, we select a specific temporal mode in the transmitted light field, resulting in a coupled master equation for the relevant mode and the chiral emitters. We characterize the mode's state by its Wigner function and show that the emission from the system predominantly produces mixtures of few-photon-added coherent states. We argue that these nonclassical states are experimentally accessible and show their application for quantum metrology.

Qubit control using quantum Zeno effect: Action principle approach

We employ the stochastic path-integral formalism and action principle for continuous quantum measurements – the Chantasri–Dressel–Jordan (CDJ) action formalism Chantasri et al., (2013; 2015) – to understand the stages in which quantum Zeno effect helps control the states of a simple quantum system. The detailed dynamics of a driven two-level system subjected to repeated measurements unravels a myriad of phases, so to say. When the detection frequency is smaller than the Rabi frequency, the oscillations slow down, eventually coming to a halt at an interesting resonance when measurements are spaced exactly by the time of transition between the two states. On the other hand, in the limit of large number of repeated measurements, the dynamics organizes itself in a rather interesting way about two hyperbolic points in phase space whose stable and unstable directions are reversed. Thus, the phase space flow occurs from one hyperbolic point to another, in different ways organized around the separatrices. We believe that the systematic treatment presented here paves the way for a better and clearer understanding of quantum Zeno effect in the context of quantum error correction.

Coalescence of non-Markovian dissipation, quantum Zeno effect, and non-Hermitian physics in a simple realistic quantum system

Diagonalization of the effective Hamiltonian describing an open quantum system is the usual method of tracking its exceptional points. Although, such a method is successful for tracking EPs in Markovian systems, it may be problematic in non-Markovian systems where a closed expression of the effective Hamiltonian describing the open system may not exist. In this work we provide an alternative method of tracking EPs in open quantum systems, using an experimentally measurable quantity, namely the effective decay rate of a qubit. The quantum system under consideration consists of two non-identical interacting qubits, one of which is coupled to an external environment. We develop a theoretical framework in terms of the time-dependent Schrodinger equation of motion, which provides analytical closed form solutions of the Laplace transforms of the qubit amplitudes for an arbitrary spectral density of the boundary reservoir. The link between the peaked structure of the effective decay rate of the qubit that interacts indirectly with the environment, and the onset of the quantum Zeno effect, is discussed in great detail revealing the connections between the latter and the presence of exceptional points. Our treatment and results have in addition revealed an intricate interplay between non-Markovian dynamics, quantum Zeno effect and non-Hermitian physics

Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance

The Exceptional Points (EPs) of non-Hermitian Hamiltonians (NHHs) are spectral degeneracies associated with coalescing eigenvalues and eigenvectors which are associated with remarkable dynamical properties. These EPs can be generated experimentally in open quantum systems, evolving under a Lindblad equation, by postselecting on trajectories that present no quantum jumps, such that the dynamics is ruled by a NHH. Interestingly, changing the way the information used for postselection is collected leads to different unravelings, i.e., different set of trajectories which average to the same Lindblad equation, but are associated with a different NHH. Here, we exploit this mechanism to create and control EPs solely by changing the measurement we postselect on. Our scheme is based on a realistic homodyne reading of the emitted leaking photons with a weak-intensity laser (a process which we call $\beta$-dyne), which we show generates a tunable NHH, that can exhibit EPs even though the system does have any in the absence of the laser. We consider a few illustrative examples pointing the dramatic effects that different postselections can have on the spectral features of the NHH, paving the road towards engineering of EPs in simple quantum systems.

Quasi-parity-time symmetric dynamics in periodically driven two-level non-Hermitian system

<sec>In recent years, there have been intensive studies of non-Hermitian physics and parity–time (PT) symmetry due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric system is phase transition (spontaneous PT-symmetry breaking), i.e. an all-real energy spectrum changes into an all-complex one when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. The generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real energy spectra is a currently important endeavor. A simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for the realization of non-unitary single-qubit quantum gate. However, studies of the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system are still relatively rare.</sec><sec></sec><sec>In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. According to these pseudo fixed points, we analytically construct a non-unitary evolution operator and then explore the dynamic behaviors of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although it is non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all-real to all-complex energy spectrum, just like the PT symmetric system. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system satisfies fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not meet such a PT symmetry, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the requirement for the PT symmetry.</sec>

Quasi-Parity-Time symmetric dynamics in a periodcially driven two-level non-Hermitian system

In recent years, there have been intensive studies on non-Hermitian physics and parity-time (PT) symmetry, due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric systems is phase transition (spontaneous PT-symmetry breaking), where the energy spectrum changes from all real to complex when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. Generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real spectra is a currently important endeavor. The simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for realization of non-unitary single-qubit quantum gate. However, studies on the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system still remain relatively rare.<br>In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. Based on these pseudo fixed points, we analytically construct the non-unitary evolution operator and then explore the dynamics of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although being non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all real to complex, just as for PT symmetric systems. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system respects fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the PT symmetry requirement.

Non Perturbative Approach to the Time Evolution of a Simple Excited Coupled Quantum System in a Cavity

Non Perturbative Approach to the Time Evolution of a Simple Excited Coupled Quantum System in a Cavity

Applications of the Numerov method to simple quantum systems using Python

Numerov’s numerical method is developed in a didactic way by using Python in its Jupyter Notebook version 6.0.3 for three different quantum physical systems: the hydrogen atom, a molecule governed by the Morse potential and a quantum dot. After a brief introduction to the Numerov method, the complete code to calculate the eigenfunctions and eigenvalues of the hydrogen atom is presented. The necessary code changes to compute the other two examples are also provided in the sequel.

Single-momentum path integral Monte Carlo simulations of uniform electron gas in warm dense matter regime

In this paper, the single-momentum path integral Monte Carlo method, previously developed for simple quantum systems and hydrogen plasma, is adapted to simulations of the uniform electron gas. The developed method is based on the combination of Wigner formalism and the path integral approach and is able to calculate various thermodynamic values and distribution functions without differentiation of the partition function. Since the exchange interaction between electrons is taken into account by the Gram determinants of the exchange matrix, the fermionic sign problem is reduced significantly, and in the case of coordinate-depending variables, is completely eliminated. The method was applied to study thermodynamic properties of the uniform electron gas in warm dense matter regime. Average kinetic, potential, and exchange-correlation energy were calculated in a wide range of states.

Considerations about the incompleteness of the Ehrenfest’s theorem in quantum mechanics

We describe a study motivated by our interest to examine the incompleteness of the Ehrenfest’s theorem in quantum mechanics and to resolve a doubt regarding whether or not the hermiticity of the Hamiltonian operator is sufficient to justify a simplification of the expression of the macroscopic-observable time derivative that promotes the one usually found in quantum-mechanics textbooks. The study develops by considering the simple quantum system ‘particle in one-dimensional box’. We propose theoretical arguments to support the incompleteness of the Ehrenfest’s theorem in the formulation he gave, in agreement with similar findings already published by a few authors, and corroborate them with the numerical example of an electric charge in an electrostatic field. The contents of this study should be useful to Bachelor and Master students; the style of the discussions is tailored to stimulate, we hope, the student’s ability for independent thinking.

The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit). However, already for a three-level system (qutrit) the state space has eight dimensions, so that its complexity exceeds the grasp of our three-dimensional space of experience. This is unfortunate, given that the geometric object describing the state space of a qutrit has a much richer structure and is in many ways more representative for a general quantum system than a qubit. In this work we demonstrate that, based on the Bloch representation of quantum states, it is possible to construct a three dimensional model for the qutrit state space that captures most of the essential geometric features of the latter. Besides being of indisputable theoretical value, this opens the door to a new type of representation, thus extending our geometric intuition beyond the simplest quantum systems.

Bosons vs. Fermions – A computational complexity perspective

Recent years have seen a flurry of activity in the fields of quantum computing and quantum complexity theory, which aim to understand the computational capabilities of quantum systems by applying the toolbox of computational complexity theory. This paper explores the conceptually rich and technologically useful connection between the dynamics of free quantum particles and complexity theory. I review results on the computational power of two simple quantum systems, built out of noninteracting bosons (linear optics) or noninteracting fermions. These rudimentary quantum computers display radically different capabilities—while free fermions are easy to simulate on a classical computer, and therefore devoid of nontrivial computational power, a free-boson computer can perform tasks expected to be classically intractable. To build the argument for these results, I introduce concepts from computational complexity theory. I describe some complexity classes, starting with P and NP and building up to the less common #P and polynomial hierarchy, and the relations between them. I identify how probabilities in free-bosonic and free-fermionic systems fit within this classification, which then underpins their difference in computational power. This paper is aimed at graduate or advanced undergraduate students with a Physics background, hopefully serving as a soft introduction to this exciting and highly evolving field.

Exact N -point-function mapping between pairs of experiments with Markovian open quantum systems

We formulate an exact spacetime mapping between the $\mathcal{N}$-point correlation functions of two different experiments with open quantum gases. Our formalism extends a quantum-field mapping result for closed systems [Phys. Rev. A \textbf{94}, 043628 (2016)] to the general case of open quantum systems with Markovian property. For this, we consider an open many-body system consisting of a $D$-dimensional quantum gas of bosons or fermions that interacts with a bath under Born-Markov approximation and evolves according to a Lindblad master equation in a regime of loss or gain. Invoking the independence of expectation values on pictures of quantum mechanics and using the quantum fields that describe the gas dynamics, we derive the Heisenberg evolution of any arbitrary $\mathcal{N}$-point function of the system in the regime when the Lindblad generators feature a loss or a gain. Our quantum field mapping for closed quantum systems is rewritten in the Schr\"odinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the $\mathcal{N}$-point functions of the open quantum system. As a concrete example of the mapping, we consider the mean-field dynamics of a simple dissipative quantum system that consists of a one-dimensional Bose-Einstein condensate being locally bombarded by a dissipating beam of electrons in both cases when the beam amplitude or the waist is steady and modulated.