Solutions to explicit time-dependent problems in quantum mechanics are rare. In fact, all known solutions are coupled to specific properties of the Hamiltonian and may be divided into two categories: One class consists of time-dependent Hamiltonians which are not higher than quadratic in the position operator, like i.e the driven harmonic oscillator with time-dependent frequency. The second class is related to the existence of additional invariants in the Hamiltonian, which can be used to map the solution of the time-dependent problem to that of a related time-independent one.
In this article we discuss and develop analytic methods for solving time-dependent tunneling problems, which cannot be addressed by using quadratic Hamiltonians. Specifically, we give an analytic solution to the problem of tunneling from an attractive time-dependent potential which is embedded in a long-range repulsive potential.
Recent progress in atomic physics makes it possible to observe experimentally time-dependent phenomena and record the probability distribution over a long range of time. Of special interest is the observation of macroscopical quantum-tunneling phenomena in Bose-Einstein condensates with time-dependent trapping potentials. We apply our model to such a case in the last section.
We consider exact time-dependent analytic solutions to the Schrödinger equation for tunneling in one dimension with cut off wave initial conditions at $t=0$. We obtain that as soon as $t \neq 0$ the transmitted probability density at any arbitrary distance rises instantaneously with time in a linear manner. Using a simple model we find that the above nonlocal effect of the time-dependent solution is suppressed by consideration of low-energy relativistic effects. Hence at a distance $x_0$ from the potential the probability density rises after a time $t_0=x_0/c$ restoring Einstein causality. Thi…
The Zeno time has been calculated for a metastable two level atom tunneling through a interacting thermal magnetic field. The process of weak measurement has been utilized for the the estimation of the timescale. The temperature dependence of the Zeno time has been shown. From the calculation it is evident that the Zeno time decreases with the increase of temperature. Moreover, the result restricts the Zeno time to a maximum limiting value, irrespective of how frequent is the measurement process.
Quantum noise with exchange and tunneling is studied within time-dependent wave packets. A novel expression for the quantum noise of two identical particles injected simultaneously from opposite sides of a tunneling barrier is presented. Such quantum noise expression provides a physical (non-spurious) explanation for the experimental detection of two electrons at the same side under static potentials. Numerical simulations of the two-particle scattering probabilities in a double barrier potential with an oscillatory well are performed. The dependence of the quantum noise on the electron energy…
It is now common practice to solve the Schrödinger equation to estimate the tunneling current between two metal electrodes at specified potentials, or the transmission through a potential barrier by assuming an incident, reflected, and transmitted wave. However, we suggest that these methods may not be appropriate for nanoscale circuits. The electron man-free path may be as long as 68.2 nm in metallic elements so we consider the possibility that quantum effects may occur throughout a nanoscale circuit, including the connections. Analytical methods are presented for modeling the coherent transf…
A new semiclassical approach to ionization by an oscillating field is presented. For a delta-function atom, an asymptotic analysis is performed with respect to a quantity h, defined as the ratio of photon energy to ponderomotive energy. This h appears formally equivalent to Planck's constant in a suitably transformed Schroedinger equation and allows semiclassical methods to be applicable. Systematically, a picture of tunneling wave packets in complex time is developped, which by interference account for the typical ponderomotive features of ionization curves. These analytical results are then …
The position-momentum uncertainty relations containing the dependence of their quantum bounds on state purity parameter $μ$ are discussed in context of possibilities to influence on the potential barrier transparency by means of decoherence processes. The behavior of barrier transparency $D$ is shown to satisfy the condition $μ^{-1}\ln D=const$. The particular case of thermal state with temperature $T$ where the purity parameter is a function of temperature is considered. For large temperature the condition for the barrier transparency is shown to be $T\ln D=const$.
Dwell time for a two state particle tunneling through a noisy thermal magnetic barrier has been calculated by studying the time evolution of the system. The effect of temperature has been included by averaging over the environmental magnetic modes. The time scale has been calculated in the framework of weak measurement. The dwell time initially increases with the rise of temperature and finally saturates. The increment of dwell time can be explained by the phenomena of quantum memory loss caused by efficient energy exchange with the environmental modes. The saturation region at higher temperat…
New time-dependent treatment of tunneling from localized state to continuum is proposed. It does not use the Laplace transform (Green's function's method) and can be applied for time-dependent potentials, as well. This approach results in simple expressions describing dynamics of tunneling to Markovian and non-Markovian reservoirs in the time-interval $-\infty<t<\infty$. It can provide a new outlook for tunneling in the negative time region, illuminating the origin of the time's arrow problem in quantum mechanics. We also concentrate on singularity at $t=0$, which affects the perturbative expa…
We propose to use a time-dependent imaginary potential to describe quantum mechanical tunneling through time-varying potential barriers. We use Gamow solutions for stationary tunneling problems to justify our choice of potential, and we apply our method to describe tunneling of a mesoscopic quantum variable: the phase change across a Josephson junction. The Josephson junction phase variable behaves as the position coordinate of a particle moving in a tilted washboard potential, and our general solution to the motion in such a potential with a time-dependent tilt reproduces a number of features…
Canonical semiclassical methods can be used to develop an intuitive definition of tunneling time through potential barriers. An application to atomic ionization is given here, considering both static and time-dependent electric fields. The results allow one to analyze different theoretical constructions proposed recently to evaluate ionization experiments based on attoclocks. They also suggest new proposals of determining tunneling times, for instance through the behavior of fluctuations.
Two-particle scattering probabilities in tunneling scenarios with exchange interaction are analyzed with quasi-particle wave packets. Two initial one-particle wave packets (with opposite central momentums) are spatially localized at each side of a barrier. After impinging upon a tunneling barrier, each wave packet splits into transmitted and reflected components. When the initial two-particle anti-symmetrical state is defined as a Slater determinant any type of (normalizable) one-particle wave packet, it is shown that the probability of detecting two (identically injected) electrons at the sam…
We show the equivalence of the functions $G_{\rm p}(t)$ and $|Ψ(d,t)|^2$ for the ``passage time'' in tunneling. The former, obtained within the framework of the real time Feynman histories approach to the tunneling time problem, using the Gell-Mann and Hartle's decoherence functional, and the latter involving an exact analytical solution to the time-dependent Schrödinger equation for cutoff initial waves.
We suggest a simple experimental method for probing antiferromagnetic spin correlations of two-component Fermi gases in optical lattices. The method relies on a spin selective Raman transition to excite atoms of one spin species to their first excited vibrational mode where the tunneling is large. The resulting difference in the tunneling dynamics of the two spin species can then be exploited, to reveal the spin correlations by measuring the number of doubly occupied lattice sites at a later time. We perform quantum Monte Carlo simulations of the spin system and solve the optical lattice dynam…
Employing the time-dependent approach, we investigate a quantum tunneling decay of many-particle systems. We apply it to a one-dimensional three-body problem with a heavy core nucleus and two valence protons. We calculate the decay width for two-proton emission from the survival probability, which well obeys the exponential decay-law after a sufficient time. The effect of the correlation between the two emitted protons is also studied by observing the time evolution of the two-particle density distribution. It is shown that the pairing correlation significantly enhances the probability for the…
Tunneling Dynamics and Time Delay in Electron Transport through Time-Dependent Barriers with Finite-Bandwidth Reservoirs
Weizmann Institute（魏茨曼科学研究所）；BCAM - Basque Center for Applied Mathematics（巴斯克应用数学中心）；Departmento de Química-Física, Universidad del País Vasco, UPV/EHU（巴斯克大学物理化学系）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基克科学基金会）
Time-Dependent Tunneling in the Thin-Barrier Limit
Arizona State University（亚利桑那州立大学）；Shanghai Jiao Tong University（上海交通大学）；Stockholm University（斯德哥尔摩大学）；KTH Royal Institute of Technology（皇家理工学院）；Massachusetts Institute of Technology（麻省理工学院）
Transient {\it time-domain resonances} found recently in time-dependent solutions to Schrödinger's equation are used to investigate the issue of the tunneling time in rectangular potential barriers. In general, a time frequency analysis shows that these transients have frequencies above the cutoff frequency associated with the barrier height, and hence correspond to non-tunneling processes. We find, however, a regime characterized by the barrier opacity, where the peak maximum $t_{max}$ of the {\it time-domain resonance} corresponds to under-the-barrier tunneling. We argue that $t_{max}$ repre…
We study the tunneling through an oscillating delta barrier. Using time periodicity of the model, the time-dependent Schrödinger equation is reduced to a simple but infinite matrix equation. Employing Toeplitz matrices methods, the infinite matrix is replaces by a $3\times 3$ matrix, allowing an analytical solution. Looking at the frequency dependence of the transmissionamplitudes, one observes a new time scale which dominates the tunneling dynamics. This time scale differs from the one previously introduced by Büttiker and Landauer. The relation between these two is discussed.
Collective quantum tunneling with time-dependent generator coordinate method
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University（重庆大学物理学院）；Department of Physics, Graduate School of Science, The University of Tokyo（东京大学理学研究科物理学专攻）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）；Quark Nuclear Science Institute, The University of Tokyo（东京大学夸克核科学研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论与数学科学中心）
We report on an implementation of the multiconfigurational time-dependent Hartree method (MCTDH) for spin-polarized fermions (MCTDHF). Our approach is based on a mapping for opera- tors in Fock space that allows a compact and efficient application of the Hamiltonian and solution of the MCTDHF equations of motion. Our implementation extends, builds on and exploits the recursive implementation of MCTDH for bosons (R-MCTDHB) package. Together with R-MCTDHB, the present implementation of MCTDHF forms the MCTDH-X package. We benchmark the accuracy of the algorithm with the harmonic interaction mode…
We introduce a scheme that combines photon-assisted tunneling by a moving optical lattice with strong Hubbard interactions, and allows for the quantum simulation of paradigmatic quantum many-body models. We show that, in a certain regime, this quantum simulator yields an effective Hubbard Hamiltonian with tunable bond-charge interactions, a model studied in the context of strongly-correlated electrons. In a different regime, we show how to exploit a correlated destruction of tunneling to explore Nagaoka ferromagnetism at finite Hubbard repulsion. By changing the photon-assisted tunneling param…
We theoretically investigate the tunneling-induced transparency (TIT) and the Autler-Townes (AT) doublet and triplet in a triple-quantum-dot system. For the resonant tunneling case, we show that the TIT induces a transparency dip in a weak-tunneling regime and no anticrossing occurs in the eigenenergies of the system Hamiltonian. However, in a strong-tunneling regime, we show that the TIT evolves to the AT splitting, which results in a well-resolved doublet and double anticrossings. For the off-resonance case, we demonstrate that, in the weak-tunneling regime, the double TIT is realized with a…
Gate-dependent offset charge shifts and anharmonicity in gatemon qubits in the weak tunneling regime
Laboratory for Physical Sciences（物理科学实验室）；Department of Physics, University of Maryland（马里兰大学物理系）；Lincoln Laboratory, Massachusetts Institute of Technology（麻省理工学院林肯实验室）；Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）
An adiabatic approximation in terms of instantaneous resonances is developed to study the steady-state and time-dependent transport of interacting electrons in biased resonant tunneling heterostructures. The resulting model consists of quantum reservoirs coupled to regions where the system is described by nonlinear ordinary differential equations and has a general conceptual interest.
Computational methods are indispensable to study the quantum dynamics of relativistic light-matter interactions in parameter regimes where analytical methods become inapplicable. We present numerical methods for solving the time-dependent Dirac equation and the time-dependent Klein-Gordon equation and their implementation on high performance graphics cards. These methods allow us to study tunneling from hydrogen-like highly charged ions in strong laser fields and Kapitza-Dirac scattering in the relativistic regime.
We show that the interaction (cross-collision) between atoms trapped in distinct sites of a double-well potential can significantly increase the atom tunneling rate for special trap configurations leading to an effective linear Rabi regime of population oscillation between the trap wells. The inclusion of cross-collisional effects significantly extends the validity of the two-mode model approach allowing it to be alternatively employed to explain the recently observed increase of tunneling rates due to nonlinear interactions.
We investigate the single-particle time evolution and two-particle quantum correlations in a one-dimensional $N$-site lattice with a site-dependent nearest neighbor tunneling function $t_α(k)=t_0[k(N-k)]^{α/2}$. Since the bandwidth and the energy levels spacings for such a lattice both depend upon $α$, we show that the observable properties of a wavepacket, such as its spread and the relative phases of its constitutents, vary dramatically as $α$ is varied from positive to negative values. We also find that the quantum correlations are exquisitely sensitive to the form of the tunneling function…
Despite quantum tunneling has been studied since the advent of quantum mechanics, the literature appears to contain no simple (textbook) formula for tunneling in generic asymmetric double-well potentials. In the regime of strong localization, we derive an succinct analytical formula based on the WKB semi-classical approach. Two different examples of asymmetric potentials are discussed: when the two localized levels are degenerate or not. For the first case, we also discuss a time-dependent problem showing quantum Zeno effect.
Using a time operator, we define a tunneling time for a particle going through a barrier. This tunneling time is the average of the phase time introduced by other authors. In addition to the delay time caused by the resonances over the barrier, the present tunneling time is also affected by the branch point at the edge of the energy continuum. We find that when the particle energy is near the branch point, the tunneling time becomes strongly dependent on the width of the incoming wave packet, which implies that there is no intrinsic tunneling time. This effect is related to the quantum uncerta…
Using the phenomenological quantum friction models introduced by Caldirola-Kanai, Kostin, and Albrecht, we study quantum tunneling of a one-dimensional potential in the presence of energy dissipation. To this end, we calculate the tunneling probability using a time-dependent wave packet method. The friction reduces the tunneling probability. We show that the three models provide similar penetrabilities to each other, among which the Caldirola-Kanai model requires the least numerical effort. We also discuss the effect of energy dissipation on quantum tunneling in terms of barrier distributions.
We use the Wick-rotated time-dependent supersymmetry to construct models of two-dimensional Dirac fermions in presence of an electrostatic grating. We show that there appears omnidirectional perfect transmission through the grating at specific energy. Additionally to being transparent for incoming fermions, the grating hosts strongly localized states.
