Noble-gas spins feature hours long coherence times owing to their great isolation from the environment, and find practical usage in various applications. However, this isolation leads to extremely slow preparation times, relying on weak spin transfer from an electron-spin ensemble. Here we propose a controllable mechanism to enhance this transfer rate. We analyze the spin dynamics of helium-3 atoms with hot, optically-excited potassium atoms and reveal the formation of quasi-bound states in resonant binary collisions. We find a resonant enhancement of the spin-exchange cross section by up to six orders of magnitude and two orders of magnitude enhancement for the thermally averaged, polarization rate-coefficient. We further examine the effect for various other noble gases and find that the enhancement is universal. We outline feasible conditions under which the enhancement may be experimentally observed and practically utilized.
Quantum tunneling through an almost classical potential barrier can be strongly enhanced by a nonstationary field so that the penetration through the barrier becomes not exponentially small. This constitutes an extremely unusual phenomenon of quantum physics called Euclidean resonance. A certain nonstationary barrier is proposed with a very low WKB tunneling rate. The quantum dynamics of this barrier is mapped on resonant tunneling across a static double barrier with a resonant level inside. The real penetration through the dynamical barrier is not exponentially small providing an example of E…
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…
Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunneling-ind…
Nonlinear resonances in the classical phase space lead to a significant enhancement of tunneling. We demonstrate that the double resonance gives rise to a complicated tunneling peak structure. Such double resonances occur in Hamiltonian systems with an at least four-dimensional phase space. To explain the tunneling peak structure, we use the universal description of single and double resonances by 4D normal-form Hamiltonians. By applying perturbative methods, we reveal the underlying mechanism of enhancement and suppression of tunneling and obtain excellent quantitative agreement. Using a mini…
We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the phase space of an integrable approximation with one nonlinear resonance chain. We evaluate the resonance-assisted contribution analytically and give a prediction based on just a few properties of the classical phase space. For the standard map excellent agreement with numerically determined tunneling rates is observed. The results should similarly apply to ioni…
An analogy between Wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field is found. Whereas in the process of Wigner tunneling an electron encounters a classically allowed regions, where a discrete energy level coincides with its energy, in the magnetic field a potential barrier is a constant in the direction of tunneling. Along the tunneling path the certain regions are formed, where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. These regions play a role of potential wells, where a discrete en…
We calculate the tunneling process of a Dirac particle across two square barriers separated a distance $d$, as well as the scattering by a double cusp barrier where the centers of the cusps are separated a distance larger than their screening lengths. Using the scattering matrix formalism, we obtain the transmission and reflection amplitudes for the scattering processes of both configurations. We show that, the presence of transmission resonances modifies the Lorentizian shape of the energy resonances and induces the appearance of additional maxima in the transmission coefficient in the range …
We describe a new mechanism of tunneling between period-two vibrational states of a weakly nonlinear parametrically modulated oscillator. The tunneling results from resonant transitions induced by the fast oscillating terms conventionally disregarded in the rotating wave approximation (RWA). The tunneling amplitude displays resonant peaks as a function of the modulation frequency; near the maxima it is exponentially larger than the RWA tunneling amplitude.
This work is devoted to the research of conditions of the dark resonance (coherent population trapping) of the interaction of the laser radiation with tunneling-coupled quantum wells. The phase sensitive dependence of dark resonances has been investigated. We obtained that destruction as well as restoration of the dark resonances of the coherent population trapping is possible in dependence on algebraic sum of the phases of exciting fields. It is shown that the phase variation of exciting fields influences on the absorption and dispersion of the probe field in a medium with quantum wells.
Transient tunneling effects in triple barrier systems are investigated by considering a time-dependent solution to the Schrödinger equation with a cutoff wave initial condition. We derive a two-level formula for incidence energies $E$ near the first resonance doublet of the system. Based on that expression we find that the probability density along the internal region of the potential, is governed by three oscillation frequencies: one of them refers to the well known Bohr frequency, given in terms of the first and second resonance energies of the doublet, and the two others, represent a coupli…
We report the first observation of bound-state proximity resonances in coupled dielectric resonators. The proximity resonances arise from the combined action of symmetry and dissipation. We argue that the large ratio between the widths is a distinctive signature of the multidimensional nature of the system. Our experiments shed light on the properties of 2D tunneling in the presence of a dissipative environment.
The extremely small probability of tunneling through an almost classical potential barrier may become not small under the action of the specially adapted non-stationary signal which selects the certain particle energy E_R. For particle energies close to this value, the tunneling rate is not small during a finite interval of time and has a very sharp peak at the energy E_R. After entering inside the barrier, the particle emits electromagnetic quanta and exits the barrier with a lower energy. The signal amplitude can be much less compared to the field of the static barrier. This phenomenon can b…
We report the first experimental observation of the resonance-assisted dynamical tunneling (RADT) in the inter-mode interaction in an asymmetric-deformed microcavity. A selection rule for strong inter-mode coupling induced by RADT was observed on angular mode numbers as predicted by the RADT theory. In addition, the coupling strength was measured to be proportional to the square of the phase-space area associated with the nonlinear resonance involved in RADT. The proportionality constant was found to depend only on the nonlinear resonance, supporting the semiclassical nature of RADT.
Probabilities of resonant tunneling through a potential barrier are compared for a rigid molecule and an excited molecule. It is shown that the resonance spectrum is mainly governed by the transmission resonance spectrum of the rigid molecule. Analytical expressions for the probability for the tunneling of the rigid molecule through a barrier allow resonance-spectrum-averaged observables, including quantum diffusion, to be estimated.
The coherent tunneling phenomenon is investigated in rectangular billiards divided into two domains by a classically unclimbable potential barrier. We show that by placing a pointlike scatterer inside the billiard, we can control the occurrence and the rate of the resonance tunneling. The key role of the avoided crossing is stressed. Keywords: chaotic tunneling, quantum billiard, delta potential, diabolical degeneracy PACS: 3.65.-w, 4.30.Nk, 5.45.+b, 73.40.Gk
We investigate the tunneling process between two symmetric stable islands of a forced pendulum Hamiltonian in the weak chaos regime. We show that when the tunneling doublet is quantized over a classical non-linear resonance the tunneling rate strongly deviates from the semiclassical prediction. This mechanism is responsible for the irregular dependence of the tunneling rate on the system parameters. The weak-chaos condition allows us to make a theoretical prediction which agrees very well with the numerical results. This opens up a possible avenue to a general theory on the dependence of quant…
Using the effective mass model for an electron and the dielectric continuum model, analytical solutions of the self-consistent Schrödinger-Poisson system of equations are obtained. Quantum mechanical theory of electronic stationary states, the oscillator strengths of quantum transitions and a method of potential profile calculation is developed for the experimentally constructed three-well resonance-tunneling structure --- a separate cascade of quantum cascade detector. For the proposed method, a comparison with the results of other methods and with the results of the experiment was carried ou…
As an extension of two-level quantum bits (qubits), multilevel systems, so-called qudits, where d represents the Hilbert space dimension, have been predicted to reduce the number of iterations in quantum computation algorithms. This has been tested in the well-known [TbPc2]0 SMM, which allowed the implementation of the Grover algorithm in a single molecular unit. In the quest for molecular systems possessing an increased number of accessible nuclear spin states, we explore herein a dimeric Tb2-SMM via single crystal μ-SQUID measurements at sub-Kelvin temperatures. We observe ferromagnetic inte…
We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given $\hbar$-regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.
This paper revisited quantum tunneling dynamics through a square double-barrier potential. We emphasized the similarity of tunneling dynamics through double-barrier and that of optical Fabry--P$\acute{e}$rot (FP) interferometer. Based on this similarity, we showed that the well-known resonant tunneling can also be interpreted as a result of matter multi-wave interference, analogous to that of FP interferometer. From this analogy, we also got an analytical finesse formula of double-barrier. Compared with that obtained numerically for a specific barrier configuration, we found that this formula …
Quantum tunneling from a thin wire or a thin film through a static potential barrier in a zero magnetic field is studied. The wire or the film should satisfy a condition of transverse quantization of levels and be inhomogeneous. Depending on a form of the inhomogeneity the tunneling scenario can dramatically differ from the conventional scheme of an exponential decay of a probability density inside the barrier. This happens due to interference of various underbarrier paths, which are collected at some points giving rise to a trans-barrier state of a large amplitude. As a result, the tunneling …
We theoretically investigate the generation of microscopic atomic NOON states, corresponding to the coherent |N,0> + |0,N> superposition with N ~ 5 particles, via collective tunneling of interacting ultracold bosonic atoms within a symmetric double-well potential in the self-trapping regime. We show that a periodic driving of the double well with suitably tuned amplitude and frequency parameters allows one to substantially boost this tunneling process without altering its collective character. The time scale to generate the NOON superposition, which corresponds to half the tunneling time and w…
We present a detailed study of the gaussian laser propagation through a dielectric system composed by two right angle prisms. We investigate the transition between the spatial coherence limit, which exhibits wave-like properties and for which the resonance phenomenon can be seen, and the decoherence limit, which exhibits particle-like properties and for which the multiple diffusion occurs. We also analyze the tunneling at critical angles. In our numerical analysis, we shall use BK7 and Fused Silica prisms and a gaussian He-Ne laser with a wavelength of 632.8 nm and beam waists of 2 mm and 200 …
We consider a symmetric double barrier heterostructure enclosing a well and propose a solution for the transmission problem using a generalized WKB approach which accounts for the amplitude suppression and phase shift due to the barriers. This approach allows us to address both off-resonance and resonance cases and, in the latter case, verify the coherent destruction of tunneling.
The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the all-purpose quantum computer. In particular, the use of temporal driving has attracted a huge interest recently as it was shown that certain fast drivings can create new topological effects, while a strong driving leads to e.g. Anderson localization physics. In this work, we focus on the intermediate regime to observe a quantum chaos transport mechanism called chaos-assisted tunneling which provides new possibilities of control f…
We present a new theoretical approach to describe the quantum behavior of a macroscopic system interacting with an external irradiation field, close to the resonant condition. Here we consider the extremely underdamped regime for a system described by a double well potential. The theory includes both: transitions from one well to the other and relaxation processes. We simulate resonant phenomena in a rf-SQUID, whose parameters lie in the range typically used in the experiments. The dependence of the transition probability W on the external drive of the system $ϕ_x$ shows three resonance peaks.…
Nuclear-spin qubits have long coherence time and are desirably applied into quantum information processing. However, the existing methods either fail to address single nucleus (such as nuclear magnetic resonance), or severely affect nuclear coherence time (such as electrical nuclear manipulation based on hyperfine stark effect, ENMHSE). Here we propose an electrical nuclear manipulation called nuclear electric resonance which can on the one hand address the single nuclear qubit, and on the other keep the long coherence time. Applying this, we construct universal quantum gates with external ele…
The fastest tunneling response in double barrier resonant structures is investigated by considering explicit analytic solutions of the time dependent Schrödinger equation. For cutoff initial plane waves, we find that the earliest tunneling events consist on the emission of a series of propagating pulses of the probability density governed by the buildup oscillations in the quantum well. We show that the fastest tunneling response comes from the contribution of incident carriers at energies different from resonance, and that its relevant time scale is given by $τ_r=π\hbar /| E-ε| $, where $ε$ i…
We considered the multiphoton resonance in the periodically driven quantum oscillator with Kerr nonlinearity in the presence of weak high-order nonlinearities. Multiphoton resonance leads to the emergence of peaks and dips in the dependence of the stationary occupations of the stable states on detuning. We demonstrated that due to high-order nonlinearities, these peaks and dips acquire additional fine structure and split into several closely spaced ones. Quasiclassically, multiphoton resonance is treated as tunneling between the regions of the oscillator phase portrait, and the fine structure …
We demonstrate strong suppression of charge dispersion in a semiconductor-based transmon qubit across Josephson resonances associated with a quantum dot in the junction. On resonance, dispersion is drastically reduced compared to conventional transmons with corresponding Josephson and charging energies. We develop a model of qubit dispersion for a single-channel resonance, which is in quantitative agreement with experimental data.
We study the interplay between the dynamics of a Bose-Einstein condensate in a double-well potential and that of an optical cavity mode. The cavity field is superimposed to the double-well potential and affects the atomic tunneling processes. The cavity field is driven by a laser red detuned from the bare cavity resonance; the dynamically changing spatial distribution of the atoms can shift the cavity in and out of resonance. At resonance the photon number is hugely enhanced and the atomic tunneling becomes amplified. The Josephson junction equations are revisited and the phase diagram is calc…
We have combined two remarkable phenomena: resonance tunneling and Anderson localization. It results in unexpected spectrum reverse to usual notions. It is demonstrated by the quantum system with chaotic distribution of potential resonance tunneling traps over the whole coordinate axis. The corresponding spectrum contains continuum of 'bound' states (Anderson's localization) and discrete tunneling resonances of unlimited wave propagation. It is in contrast to the usual situation with discrete bound and continuum of scattering states.
We study the impact of coherently generated lattice photons on an atomic Mott insulator subjected to a uniform force. Analogous to an array of tunnel-coupled and biased quantum dots, we observe sharp, interaction-shifted photon-assisted tunneling resonances corresponding to tunneling one and two lattice sites either with or against the force, and resolve multiorbital shifts of these resonances. By driving a Landau-Zener sweep across such a resonance, we realize a quantum phase transition between a paramagnet and an antiferromagnet, and observe quench dynamics when the system is tuned to the cr…
In this paper we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths $\ell_\pm$ separated by a window of length 2a. It is known that if the barriers are semiinfinite, i.e. we have two adjacent waveguides coupled laterally through the boundary window, the system has for any a>0 a finite number of eigenvalues below the essential spectrum threshold. Here we demonstrate that for large but finite $\ell_\pm$ the system has resonances which converge to the said eigenvalues as $\ell_\pm\to\infty$, and derive the leading term in the …
We study the influence of a linear energy bias on a non-equilibrium excitation on a chain of molecules coupled to local phonons (a tilted Holstein model) using both a random-walk rate kernel theory and a nonperturbative, massively parallelized adaptive-basis algorithm. We uncover structured and discrete vibronic resonance behavior fundamentally different from both linear response theory and homogeneous polaron dynamics. Remarkably, resonance between the phonon energy $\hbarω$ and the bias $δ_ε$ occurs not only at integer but also fractional ratios $δ_ε/(\hbarω) = \frac{m}{n}$, which effect lon…
We discuss a generalized Schrödinger operator in $L^2(\mathbb{R}^d), d=2,3$, with an attractive singular interaction supported by a $(d-1)$-dimensional hyperplane and a finite family of points. It can be regarded as a model of a leaky quantum wire and a family of quantum dots if $d=2$, or surface waves in presence of a finite number of impurities if $d=3$. We analyze the discrete spectrum, and furthermore, we show that the resonance problem in this setting can be explicitly solved; by Birman-Schwinger method it is cast into a form similar to the Friedrichs model.
We consider the prototypical deuterium-tritium fusion reaction. At intermediate initial kinetic energies (in the keV regime), a major bottle-neck of this reaction is the Coulomb barrier between the nuclei, which is overcome by tunneling. Here, we study whether the tunneling probability can be enhanced by an additional electromagnetic field, such as an x-ray free electron laser (XFEL). We find that this dynamical assistance should be feasible with present-day or near future technology.
We theoretically explore the tunneling dynamics for the tight-binding (TB) model of a single spin-orbit-coupled atom trapped in an optical lattice subjected to lattice shaking and to time-periodic Zeeman field. By means of analytical and numerical methods, we demonstrate that the spin-orbit (SO) coupling adds some new results to the tunneling dynamics in both multiphoton resonance and far-off-resonance parameter regimes. When the driving frequency is resonant with the static Zeeman field (multi-photon resonances), we obtain an unexpected new dynamical localization (DL) phenomenon where the sin…
We consider tunneling to the continuum in a multi-dimensional potential. It is demonstrate that this problem can be treated as two separate problems: a) a bound state and b) a non-resonance scattering problem, by a proper splitting of the potential into two components. Finally we obtain the resonance energy and the partial tunneling widths in terms of the bound and the scattering state wave functions. This result can be used in a variety of tunneling problems. As an application we consider the ionization of atomic states by an external field. We obtain very simple analytical expressions for th…
