For an asymmetric double-well potential system, it is shown that, if the potential is quadratic until it reaches several times of the zero-point energies from the bottoms in each well, the energy eigenvalues of the low lying excited states of the double-well system must be close to the eigenvalues of the quadratic potentials. These eigenvalue structures suggest a method for the coherent control of the tunneling as well as realizing almost complete localization of the wave packet in one of the wells, by handling the double-well asymmetry. Numerical examples are included to indicate that the method could be useful also in a more general potential, and to propose experimental confirmations.
A new route to coherent destruction of tunneling is established by considering a monochromatic fast modulation of the self-interaction strength of a many-boson system. The modulation can be tuned such that only an arbitrarily, a priori prescribed number of particles are allowed to tunnel. The associated tunneling dynamics is sensitive to the odd or even nature of the number of bosons.
We study theoretically two coupled periodically-curved optical waveguides with Kerr nonlinearity. We find that the tunneling between the waveguides can be suppressed in a wide range of parameters due to nonlinearity. Such suppression of tunneling is different from the coherent destruction of tunneling in a linear medium, which occurs only at the isolated degeneracy point of the quasienergies. We call this novel suppression nonlinear coherent destruction of tunneling.
Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support quantum mechanical zero mode and first excited state analytical solutions. Reporting about a symmetry breaking that supports the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state, two inequivalent topological scenarios are supposed to drive stable tunneling and coherent tunneling destruction respectively. A complete pr…
An optical realization of the phenomenon of many-body coherent destruction of tunneling, recently predicted for interacting many-boson systems by Gong, Molina and Haenggi [Phys. Rev. Lett. 103, 133002 (2009)], is proposed for light transport in engineered waveguide arrays. The optical system enables a direct visualization in Fock space of the many-body tunneling control process
We study the tunneling of Dirac fermions in graphene through a double barrier potential allowing the carriers to have an effective mass inside the barrier as generated by a lattice miss-match with the boron nitride substrate. The consequences of this gap opening on the transmission are investigated. The realization of resonant tunneling conditions is also analyzed.
Discrete breathers (DBs) -- a spatial time-periodic localization of energy -- are predicted in a large variety of non-linear systems. Motivated by the conceptual bridging of the DBs phenomena in classical and quantum mechanical representation, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in a phase space -- a coherent state. We show that in contrast to a point in a phase space that can exhibit either delocalized or localized motion, a coherent state can show signatures of a quantum equivalent of both localized and delocalized behavior. In cl…
We study a system of three coherently coupled states, where one state is shifted periodically against the other two. We discover such a system possesses a dark Floquet state at zero quasienergy and always with negligible population at the intermediate state. This dark Floquet state manifests itself dynamically in terms of the suppression of inter-state tunneling, a phenomenon known as coherent destruction of tunneling. We suggest to call it dark coherent destruction of tunneling (DCDT). At high frequency limit for the periodic driving, this Floquet state reduces to the well-known dark state wi…
We investigate quantum tunneling in smooth symmetric and asymmetric double-well potentials. Exact solutions for the ground and first excited states are used to study the dynamics. We introduce Wigner's quasi-probability distribution function to highlight and visualize the non-classical nature of spatial correlations arising in tunneling.
We propose an asymmetric double quantum well structure with a common continuum and investigate the effect of resonant tunneling on the control of coherent electron population transfer between the two quantum wells. By numerically solving the motion equations of element moments, the almost complete electron population transfer from initial subband to the target subband could be realized due to the constructive interference via flexibly adjusting the structure parameters.
We investigate the dynamical phase transition of two-component Bose-Einstein condensate with nonlinear tunneling, which is trapped inside a double-well and dispersively coupled to a single mode of a high-finesse optical cavity with one moving end mirror driven by a single mode standing field. The nonlinear tunneling interaction leads to an increase of stability points and riches the phase diagram of the system. It is shown that the appearance of the moving end mirror speeds up the tunneling of Bose-Einstein condensates, which makes population difference between two wells and regulates the numb…
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…
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 …
We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a one- dimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially prepared in the left well, we increase the width of the right well in subsequent trap realizations and witness how the tunneling oscillations evolve into particle loss. In this closed system, we analyze the spectral signatures of single- and two-particle tunneling for the entire range of repulsive interactions. We conclude that for comparable widths of the two wel…
Resonant tunneling through identical potential barriers is a textbook problem in quantum mechanics. Its solution yields total transparency (100% tunneling) at discrete energies. This dramatic phenomenon results from coherent interference among many trajectories, and it is the basis of transport through periodic structures. Resonant tunneling of electrons is commonly seen in semiconducting 'quantum dots'. Here we demonstrate that detecting (distinguishing) electron trajectories in a quantum dot (QD) renders the QD nearly insulating. We couple trajectories in the QD to a 'detector' by employing …
We show that the probability distribution of the stationary state of a dissipative ac-driven two-level system exhibits discontinuities, i.e. jumps, for parameters at which coherent destruction of tunneling takes place. These discontinuities can be observed as jumps in the emission of the Mollow triplet. The jumps are the consequence of discontinuities in the transition rates, which we calculate numerically and analytically based on the secular Floquet-Redfield formalism.
Qubits driven by resonant strong pulses are studied and a parameter regime is explored in which the dynamics can be solved in closed form. Instantaneous coherent destruction of tunneling can be seen for longer pulses, whereas shorter pulses allow a fast preparation of the qubit state. Results are compared with recent experiments of pulsed nitrogen-vacancy center spin qubits in diamond.
Quantum tunneling is the quantum-mechanical effect where a particle tunnels through a classically forbidden region. Double Square Well Potential (DSWP) is a system where this phenomenon is feasible. Numerous phenomena can be illustrated by considering motion in a pair of wells that are separated by a barrier of finite height and width. The energy level splitting, resulting from barrier penetration, is the reason of the so-called inversion spectrum, which is an example of quantum tunneling. Out of several molecules ($NH_3$, $PH_3$, $AsH_3$, $NH_2CN$) where this inversion phenomenon occurs, ammo…
The macroscopic tunneling of an optomechanical membrane is considered. A cavity mode which couples quadratically to the membranes position can create highly tunable adiabatic double-well potentials, which together with the high Q-factors of such membranes render the observation of macroscopic tunneling possible. A suitable, pulsed measurement scheme using a linearly coupled mode of the cavity for the verification of the effect is studied.
The level splitting formula of an asymmetric double well potential is calculated taking into account the multi-instanton contributions (dilute gas approximation). Results can be related with known semiclassical ones obtained with a truncated hamiltonian, and the symmetric case is easily recovered.
We study the tunneling of a two-level atom in a double well potential while the atom is coupled to a single electromagnetic field mode of a cavity. The coupling between internal and external degrees of freedom, due to the mechanical effect on the atom from photon emission into the cavity mode, can dramatically change the tunneling behavior. We predict that in general the tunneling process becomes quasiperiodic. In a certain regime of parameters a collapse and revival of the tunneling occurs. Accessing the internal degrees of freedom of the atom with a laser allows to coherently manipulate the …
We report on the experimental realization of a photonic system that simulates the one-dimensional two-particle Hubbard model. This analogy is realized by means of two-dimensional arrays of coupled optical waveguides, fabricated using femtosecond laser inscription. By tuning the analogous "interaction strength", we reach the strongly-interacting regime of the Hubbard Hamiltonian, and demonstrate the suppression of standard tunneling for individual "particles". In this regime, the formation of bound states is identified through the direct observation of pair tunneling. We then demonstrate the co…
We study the interaction-modulated tunneling dynamics of a Bose-Einstein condensate (BEC) in a deep double-well potential, where the tunneling between the two wells is modulated by another BEC trapped in a harmonic potential symmetrically positioned at the center of the double-well potential. The inter-species interactions couple the dynamics of the two BECs, which give rise to interesting features in the tunneling oscillations. Adopting a two-mode approximation for the BEC in the double-well potential and coupling it with the Gross-Pitaevskii equation of the harmonically trapped BEC, we numer…
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.
We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensiti…
We report on a direct visualization of coherent destruction of tunneling (CDT) of light waves in a double well system which provides an optical analog of quantum CDT as originally proposed by Grossmann, Dittrich, Jung, and Hanggi [Phys. Rev. Lett. {\bf 67}, 516 (1991)]. The driven double well, realized by two periodically-curved waveguides in an Er:Yb-doped glass, is designed so that spatial light propagation exactly mimics the coherent space-time dynamics of matter waves in a driven double-well potential governed by the Schrödinger equation. The fluorescence of Er ions is exploited to image t…
Two main mechanisms dictate the tunneling process in a double quantum dot: overlap of excited wave functions, effectively described as a tunneling rate, and phonon-assisted tunneling. In this paper, we study different regimes of tunneling that arise from the competition between these two mechanisms in a double quantum dot molecule immersed in a unimodal optical cavity. We show how such regimes affect the mean number of excitations in each quantum dot and in the cavity, the spectroscopic resolution and emission peaks of the photoluminescence spectrum, and the second-order coherence function whi…
A general coherent control scenario to suppress, or accelerate, tunneling of quantum states decaying into a continuum, is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling (DD) protocols and sequences …
We have investigated how the dynamics of a quantum particle initially localized in the left boundary site under periodic driving can be manipulated via control of the right boundary site of a lattice array. Because of the adjustable coupling between the right boundary site and its nearest-neighbor, we can realize either coherent destruction of tunneling to coherent tunneling (CDT-CT) transition or coherent tunneling to coherent destruction of tunneling (CT-CDT) transition, by driving or moving the right boundary site while keeping the left boundary site driven by a periodically oscillating fie…
We report the observation of nonclassical light generated via photon blockade in a photonic crystal cavity with a strongly coupled quantum dot. By tuning the frequency of the probe laser with respect to the cavity and quantum dot resonance we can probe the system in either photon blockade or photon-induced tunneling regime. The transition from one regime to the other is confirmed by the measurement of the second order correlation that changes from anti-bunching to bunching.
We report on the first direct observation of coherent control of single particle tunneling in a strongly driven double well potential. In our setup atoms propagate in a periodic arrangement of double wells allowing the full control of the driving parameters such as frequency, amplitude and even the space-time symmetry. Our experimental findings are in quantitative agreement with the predictions of the corresponding Floquet theory and are also compared to the predictions of a simple two mode model. Our experiments reveal directly the critical dependence of coherent destruction of tunneling on t…
Tunneling of electrons through a barrier with complex potential is investigated. We focus on two cases, symmetric double rectangular barrier and double delta potential barrier, and give expressions for resonant transmission probability for both cases. Expressions for reflection amplitude and absorption are also obtained in the case of delta potential. It will be shown that for given dimensions of the potential barrier and the real part of the potential, resonant transmission probability approaches infinity for only one positive value of the imaginary part of the potential.
The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian approach. The estimates concern a Xe atom in a biased double-well junction potential. The exact treatment shows that quantum coherence oscillations of the metastable ground state may occur at particular resonant values of the bias voltage. The effect of decoherence by partial localization is studied within the quasi-classical frame.
We unravel the correlated tunneling dynamics of a mass imbalanced few-body fermi-fermi mixture upon quenching the tilt of a double-well. The non-equilibrium dynamics of both species changes from Rabi-oscillations close to the non-interacting limit to a delayed tunneling dynamics for moderate interspecies repulsions. Considering strong interspecies interactions the lighter species experiences quantum self-trapping due to the heavier species which acts as an effective material barrier, while performing almost perfect Rabi-oscillations. The degree of entanglement, inherent in the system, is analy…
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.
We explore the coherent destruction of tunneling (CDT) in a lattice array under selective in-phase harmonic modulations, in which some selected lattice sites are driven by in-phase harmonic oscillating fields and other lattice sites are undriven. Due to the occurrence of CDT, if the driving amplitude $A$ and the driving frequency $ω$ are tuned to satisfy the zeroth-order Bessel function $J_0(A/ω)=0$, the driven lattice sites are approximately decoupled with the undriven lattice sites. The CDT even takes place in lattice systems with high-order couplings between non-nearest lattice sites. By us…
A scheme based on Coherent Tunneling by Adiabatic Passage (CTAP) of exchange-only spin qubit quantum states in a linearly arranged double quantum dot chain is demonstrated. Logical states for the qubit are defined by adopting the spin state of three electrons confined in a double quantum dot. The possibility to obtain gate operations entirely with electrical manipulations makes this qubit a valuable architecture in the field of quantum computing for the implementation of quantum algorithms. The effect of the external control parameters as well as the effect of the dephasing on the coherent tun…
The use of adiabatic passage techniques to mediate particle transport through real space, rather than phase space is becoming an interesting possibility. We have investigated the properties of Coherent Tunneling Adiabatic Passage (CTAP) with alternating tunneling matrix elements. This geometry, not previously considered in the donor in silicon paradigm, provides an interesting route to long-range quantum transport. We introduce simplified coupling protocols, and transient eigenspectra as well as a realistic gate design for this transport protocol. Using a pairwise treatment of the tunnel coupl…
We predict wide-band suppression of tunneling of spin-orbit-coupled atoms (or noninteracting Bose-Einstein condensate) in a double-well potential with periodically varying depths of the potential wells. The suppression of tunneling is possible for a single state and for superposition of two states, i.e. for a qbit. By varying spin-orbit coupling one can drastically increase the range of modulation frequencies in which an atom remains localized in one of the potential wells, the effect connected with crossing of energy levels. This range of frequencies is limited because temporal modulation may…
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 study the dynamics of a particle tunneling between the ground states of a symmetric double potential well system, in the presence of simultaneous diagonal and non-diagonal couplings to an Ohmic oscillator bath. We use the noninteracting-blip approximation to investigate coherence effects across a wide range of system-environment coupling strengths at physiological temperatures. We show how the presence of a non-diagonal coupling mechanism significantly alters the dynamics of the tunneling particle, producing coherent oscillations despite strong thermal fluctuations in the environment. Fluct…
In this work we revisit the Salecker-Wigner-Peres clock formalism and show that it can be directly applied to the phenomenon of tunneling. Then we apply this formalism to the determination of the tunneling time of a non relativistic wavepacket, sharply concentrated around a tunneling energy, incident on a symmetric double barrier potential. In order to deepen the discussion about the generalized Hartmann effect, we consider the case in which the clock runs only when the particle can be found inside the region \emph{between} the barriers and show that, whenever the probability to find the parti…
We measured the shot noise in fully epitaxial Fe/MgAl2OX/Fe-based magnetic tunneling junctions (MTJs). While the Fano factor to characterize the shot noise is very close to unity in the antiparallel configuration, it is reduced to 0.98 in the parallel configuration. This observation shows the sub-Poissonian process of electron tunneling in the parallel configuration, indicating the coherent tunneling through the spinel-based tunneling barrier of the MTJ.
We perform photon-assisted-tunneling (PAT) experiments on a GaAs double quantum dot device under high microwave excitation power. Photon-assisted absorption of up to 14 photons is observed, when electron temperature (>1K) are far above the lattice temperature. Signatures of Landau-Zener-Stückelberg (LZS) interference are found even in this non-equilibrium PAT spectrum. In addition, the charge state relaxation time T_1~8ns measured in this out of thermal equilibrium double quantum dot is in agreement with other previous reports.
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the potential, semi-classical approximation at large distances and a description of tunneling under the barrier. It provides 9-10 significant digits in energies and gives for wavefunctions the relative deviation in real $x$-space less than $\lesssim 10^{-3}$.
We analyze the dynamical evolution of the resonant tunneling of an ensemble of electrons through a double barrier in the presence of the self-consistent potential created by the charge accumulation in the well. The intrinsic nonlinearity of the transmission process is shown to lead to oscillations of the stored charge and of the transmitted and reflected fluxes. The dependence on the electrostatic feedback induced by the self-consistent potential and on the energy width of the incident distribution is discussed.
Klein tunneling and conductance for Dirac fermions in ABC-stacked trilayer graphene (ABC-TLG) through symmetric and asymmetric double potential barriers are investigated using the two and six-band continuum model. Numerical results for our system show that the transport is sensitive to the height, the width and the distance between the two barriers. Klein paradox at normal incidence and resonant features at non-normal incidence in the transmission result from resonant electron states in the wells or hole states in the barriers and strongly influence the ballistic conductance of the structures.
Three level atom optics (TLAO) is introduced as a simple, efficient and robust method to coherently manipulate and transport neutral atoms. The tunneling interaction among three trapped states allows to realize the spatial analog of the stimulated Raman adiabatic passage (STIRAP), coherent population trapping (CPT), and electromagnetically induced transparency (EIT) techniques. We investigate a particular implementation in optical microtrap arrays and show that under realistic parameters the coherent manipulation and transfer of neutral atoms among dipole traps could be realized in the millise…
We have studied dynamical properties and quantum tunneling in asymmetric double-well (DW) systems, by solving Schrödinger equation with the use of two kinds of spectral methods for initially squeezed Gaussian wavepackets. Time dependences of wavefunction, averages of position and momentum, the auto-correlation function, an uncertainty product and the tunneling probability have been calculated. Our calculations have shown that (i) the tunneling probability is considerably reduced by a potential asymmetry $ΔU$, (ii) a resonant tunneling with $|ΔU| \simeq κ\:\hbar ω$ is realized for motion starti…
In the spectrum of systems showing chaos-assisted tunneling, three-state crossings are formed when a chaotic singlet intersects a tunnel doublet. We study the dissipative quantum dynamics in the vicinity of such crossings. A harmonically driven double well coupled to a bath serves as a model. Markov and rotating-wave approximations are introduced with respect to the Floquet spectrum of the time-dependent central system. The resulting master equation is integrated numerically. We find various types of transient tunneling, determined by the relation of the level width to the inherent energy scal…
Photon emission by tunneling electrons can be encouraged by locating a resonator close to the tunnel junction and applying an appropriate voltage-bias. However, studies of normal metals show that the resonator also affects how the charges flow, facilitating processes in which correlated tunneling of two charges produces one photon. We develop a theory to analyze this kind of behavior in Josephson junctions by deriving an effective Hamiltonian describing processes where two Cooper-pairs generate a single photon. We determine the conditions under which the transport is dominated by incoherent tu…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $ω$ and the difference of the minima is close to a multiple of $\hbar ω$. A WKB wave function is constructed on both sides of the local maximum between the wells, by matching the WKB function to the exact wave functions near the classical turning points. The continuities of the wave function and its first derivative at the local maximum then give the energy-level splitting formula, which not only reproduces the instanton result for a symmetric potential, but also elucidates t…
We study the stabilization of coherent suppression of tunneling in a driven double-well system subject to random periodic $δ-$function ``kicks''. We model dissipation due to this stochastic process as a phase diffusion process for an effective two-level system and derive a corresponding set of Bloch equations with phase damping terms that agree with the periodically kicked system at discrete times. We demonstrate that the ability of noise to localize the system on either side of the double-well potenital arises from overdamping of the phase of oscillation and not from any cooperative effect be…
The dynamics of the population imbalance of bosons in a double-well potential is investigated from the point of view of many-body quantum mechanics in the framework of the two-mode model. For small initial population imbalances, coherent superpositions of almost equally spaced energy eigenstates lead to Josephson oscillations. The suppression of tunneling at population imbalance beyond a critical value is related to a high concentration of initial state population in the region of the energy spectrum with quasi-degenerate doublets resulting in imbalance oscillations with a very small amplitude…
