Coherent Destruction Of Tunneling Research Articles

Utilizing the multifrequency resonances of the electron spins in diamond nitrogen-vacancy centers under strong radio frequency driving for quantum sensing

Multifrequency resonances in the pulsed-optically detected magnetic resonance (ODMR) spectra of electron spins in ensemble nitrogen-vacancy (NV) centers in diamonds are investigated under strong radio frequency (RF) driving at a MHz frequency range and weak microwave driving at a GHz frequency range in a bias static magnetic field for quantum sensing applications. First, we demonstrate that the coherent destruction of tunneling, which leads to the disappearance of the main resonance peaks, can be utilized for precise calibration of the RF amplitude. Next, we clarify the condition for enhancing the sensitivity of a DC magnetic field under strong RF driving at the RF frequency that matches the split frequency due to the hyperfine interaction between 15N nuclear spins and the NV electron spins. Our findings indicate that strong RF driving increases the sensitivity of the DC magnetic field by enhancing the ODMR contrast and reducing the linewidth. The above results contribute to certifying the quantitative accuracy of RF imaging and enhancing the sensitivity of the DC magnetic field imaging using ensemble NV centers in diamonds.

Spin–orbit coupling effects on localization and correlated tunneling for two interacting bosons in a double-well potential

We theoretically study the tunneling dynamics of two interacting spin–orbit-coupled (SOC) atoms trapped in a periodically perturbed double-well potential. We find that the phenomenon of coherent destruction of tunneling (CDT) can exist only for certain values of SOC, and two different mechanisms for the appearance of CDT are identified in this system. One is the conventional CDT resulting from quasi-energy degeneracy, while the other CDT originates from the dark Floquet state with zero quasi-energy for all values of the driving parameters. We discover that under double modulation combining the double-well potential shaking and a time-periodic Zeeman field, it is possible to realize spin-flipping single-atom Rabi tunneling and the CDT induced by the dark Floquet state at any value of SOC strength, which is not accessible with a single-drive field. Furthermore, we show that the detuning of Zeeman field with respect to the multiphoton energy is particularly significant in the case of the correlated two-particle tunneling mediated by SOC. We expect that these results will stimulate further exploration of the many-body dynamics in the interacting systems and expand the possibilities for manipulating the spin dynamics.

Quantum tunneling dynamics with robust reciprocity of Bose-Einstein condensate in a quadruple-well potential with synthetic gauge fields

Bose-Einstein condensation (BEC) trapped in quadruple-well potential with complex coupling provides a great useful platform in theoretical and experimental researches. Utilizing analytical and numerical methods, we investigate tunneling dynamics and the reciprocity of quantum transport of BEC in quadruple-well potential formed by the laser-assisted transition. According to the investigation, the tunneling dynamics of BEC in this system is independent of dissipation and complex coupling between wells caused by Raman coupling laser. By adjusting the coupling phase, the coherent destruction of tunneling can be observed. Meanwhile, this system provides an applicable proposal for reciprocal quantum switch by using the tunneling dynamics of BEC.

Coherent destruction of tunnelling in a symmetrical double well driven by a series of time dependent δ functions

It is analytically and numerically shown that the coherent tunnelling between the individual wells of a symmetrical double well potential can be totally suppressed when it is driven by a periodic series of δ function in time, depending on the time period and strength of the δ function. We have applied time dependent perturbation theory to have an understanding over the process. In absence of any kind of perturbation, the average position of the particle makes a sinusoidal oscillation between two wells. With the application of a periodic δ function, the amplitude and the frequency of the oscillation both get modified. In this article we have explored how the frequency and strength of the applied perturbation controls the quantum dynamics of tunnelling and finally, how these parameters drive the system towards a complete stand still situation, which is described as coherent destruction of tunnelling.

Dynamic resonant tunneling via a quasibound superstate

The quantum tunneling current via an opaque barrier with an oscillating well reveals a wealth of physical phenomena: eigenstate-assisted activation, the elevator effect, coherent destruction of tunneling, suppression of activation, and the Sisyphus effect are a few examples. In this paper, we investigate these effects from a different perspective---transmission via a quasibound super state (QBSS). It is shown that an oscillating well supports a QBSS, which consists of numerous quasibound substates. Each one of these substates has a finite spectral width, which corresponds to the escape probability. However, they construct a unique spectrum, which consists of activated and suppressed quasi substates all of which are simultaneously excited. Thus, when the oscillating well is integrated into an opaque barrier, one can borrow an analogy from stationary resonant tunneling (RT). In the stationary RT scenario, current flows via a quasibound state. In the oscillating RT scenario, current flows via a QBSS. This analogy can easily explain many of the system's complex behaviors: the symmetry between the current's sensitivity to the incoming energy and the outgoing one, and even why some frequencies induce activation while others suppress it. This analogy can be applied to improve the sensitivity of the system when used for a frequency-controlled transistor for it predicts that when the incoming energy is shifted from the central resonance of the QBSS, the device's current becomes exponentially sensitive to the applied frequency. While the oscillations' frequency mainly determines the spectral distance between substates, the oscillations' amplitude determines the spectral width and center of the QBSS. Furthermore, it is suggested that this analogy can be applied to investigate microbiological systems (the olfactory system) and optical devices.

Statistics of interferograms in three-level systems

We report on the high-frequency (HF) regime of a microwave (MW) pulse consisting of a superimposition of N harmonics acting transversally on a three-level system (ThLS) simultaneously driven in the longitudinal direction by a radio-frequency (RF) signal and in the presence of a zero-energy splitting term D(Sz)2 where D denotes the uniaxial anisotropy and Sz the projection of the spin-1 vector along the quantization direction. We carry out the study by numerical simulations of the Bloch equation (in the absence of relaxation) and present the associated interference patterns for various combinations of the system's parameters. We have established that at high frequencies, the MW opens 2N windows for replication of the action of the RF on the interferograms. The ThLS exhibits multiple (N successive) coherent destruction of tunneling (CDT) when the RF drives it to avoided level crossings where it undergoes Landau-Zener-Stückelberg-Majorana (LZSM) transitions. These CDT are centered at resonance points where D matches the characteristic frequencies of the counter-rotating and rotating terms in the MW pulse. The effects observed are explained by invoking the rotating wave approximation and the Floquet theory. Our analytical results are found in satisfactory agreement with numerics. We have equally observed an infinite multiplication of interferograms for a bichromatic RF pulse when the characteristic amplitude and frequency of the additional signal are large even in the absence of a periodic MW pulse.

Observation of Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems.

Periodically driven (Floquet) quantum systems have recently been a focus of nonequilibrium physics by virtue of their rich dynamics. Time-periodic systems not only exhibit symmetries that resemble those in spatially periodic systems, but also display novel behavior that arises from symmetry breaking. Characterization of such dynamical symmetries is crucial, but often challenging due to limited driving strength and lack of an experimentally accessible characterization technique. Here, we show how to reveal dynamical symmetries, namely, parity, rotation, and particle-hole symmetries, by observing symmetry-induced Floquet selection rules. Notably, we exploit modulated driving to reach the strong light-matter coupling regime, and we introduce a protocol to experimentally extract the transition matrix elements between Floquet states from the system coherent evolution. By using nitrogen-vacancy centers in diamond as an experimental test bed, we execute our protocol to observe symmetry-protected dark states and dark bands, and coherent destruction of tunneling. Our work shows how one can exploit the quantum control toolkit to study dynamical symmetries that arise in the topological phases of strongly driven Floquet systems.

Dynamics of quantum systems driven by time-varying Hamiltonians: Solution for the Bloch-Siegert Hamiltonian and applications to NMR

Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalisation of the Hamiltonian do not work in this setting. In fact, since the inception of Magnus' expansion in 1954, no fundamentally novel mathematical approach capable of solving the quantum equations of motion with a time-varying Hamiltonian has been devised. We report here of an entirely different non-perturbative approach, termed path-sum, which is always guaranteed to converge, yields the exact analytical solution in a finite number of steps for finite systems and is invariant under scale transformations of the quantum state space. Path-sum can be combined with any state-space reduction technique and can exactly reconstruct the dynamics of a many-body quantum system from the separate, isolated, evolutions of any chosen collection of its sub-systems. As examples of application, we solve analytically for the dynamics of all two-level systems as well as of a many-body Hamiltonian with a particular emphasis on NMR (Nuclear Magnetic Resonance) applications: Bloch-Siegert effect, coherent destruction of tunneling and $N$-spin systems involving the dipolar Hamiltonian and spin diffusion.

Robust Diabatic Grover Search by Landau–Zener–Stückelberg Oscillations

Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau–Zener–Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is , which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.

Observation of robust flat-band localization in driven photonic rhombic lattices.

We demonstrate that a flat-band state in a quasi-one-dimensional rhombic lattice is robust in the presence of external drivings along the lattice axis. The lattice was formed by periodic arrays of evanescently coupled optical waveguides, and the external drivings were realized by modulating the paths of the waveguides. We excited a superposition of flat-band eigenmodes at the input and observed that this state does not diffract in the presence of static, as well as high-frequency sinusoidal drivings. This robust localization is due to destructive interference of the analogous wavefunction and is associated with the symmetry in the lattice geometry. We then excited the dispersive bands and observed Bloch oscillations and coherent destruction of tunneling.

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and helpful for illuminating some generalizations of appealing concepts originating in the Hermitian system. Some intriguing physical phenomena, such as stabilization of a non-Hermitian system by periodic driving, non-Hermitian analogs of coherent destruction of tunneling (CDT) and complete population inversion (CPI), are demonstrated analytically and confirmed numerically. In addition, by using these exact solutions we derive a pulse area theorem for such non-Hermitian CPI in the parity-time symmetric two-level system. Our results may provide an additional possibility for pulse manipulation and coherent control of the parity-time symmetric two-level system.

Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguides

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 coherent destruction of tunneling (CDT) for the paired particles in the presence of an engineered oscillating force of high frequency. The precise control over the analogous "interaction strength" and driving force offered by our experimental system opens an exciting route towards quantum simulation of few-body physics in photonics.

Tunnelling of spin-orbit coupled Bose-Einstein condensates in driven double-well potential

The tunnelling dynamics of spin-orbit (SO) coupled Bose-Einstein condensates in a periodically driven double-well potential are investigated both theoretically and numerically. We find that, when the SO coupling is absent, the atomic interactions suppress the tunnelling (as in usual Bose-Einstein condensed system), and the Zeeman field does not influence the usual tunnelling. When the SO coupling is present, the coupling of the atomic interactions and the Zeeman-field intensity can either enhance or suppress the tunnelling. The system undergoes rich transformations from the coherent tunnelling (CT) to the coherent destruction of tunnelling (CDT) when the SO coupling or the atomic interactions or the Zeeman-field intensity changes. In high-frequency region, the triangular structure and the circle structure are revealed in quasi-energy bands of the system, the width of the triangular structure or the circle structure and the localization width are relevant. And the SO coupling modifies traditional degenerate modes of quasi-energy bands. The results provide a possible way to control the usual tunnelling and the spin-flipping tunnelling in double-well potential.

Coherent destruction of tunneling in two-level system driven across avoided crossing via photon statistics.

In this paper, the nature of the multi-order resonance and coherent destruction of tunneling (CDT) for two-level system driven cross avoided crossing is investigated by employing the emitted photons 〈N〉 and the Mandel’s Q parameter based on the photon counting statistics. An asymmetric feature of CDT is shown in the spectrum of Mandel’s Q parameter. Also, the CDT can be employed to suppress the spontaneous decay and prolong waiting time noticeably. The photon emission pattern is of monotonicity in strong relaxation, and homogeneity in pure dephasing regime, respectively.

Effective Hamiltonians for Rapidly Driven Many-Body Lattice Systems: Induced Exchange Interactions and Density-Dependent Hoppings.

We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g., Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered, where our corrections play an essential role.

Coherent revival of tunneling

We introduce a tunneling effect by a driving field, referred to as coherent revival of tunneling (CRT), corresponding to complete tunneling (transmission coefficient $=1$) that is revived from the circumstance of total reflection (transmission coefficient $\ensuremath{\approx}0$) through application of an appropriate perpendicular high-frequency ac field. To illustrate CRT, we simulate electron transport through fish-bone-like quantum-dot arrays by using single-particle Green's functions along with Floquet theory, and we explore the corresponding current-field amplitude characteristics as well as current-polarization characteristics. In regard to the two characteristics, we show that CRT exhibits entirely different features than coherent destruction of tunneling and photon-assisted tunneling. We also discuss two practical conditions for experimental realization of CRT.

Coherent destruction of tunneling in a lattice array with a controllable boundary

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 field with a fixed driving parameter. In particular, the transition direction shows odd-even sensitivity to the number of lattice sites. We have also revealed that our proposed CDT-CT transition is robust against the second order coupling (SOC) between next-nearest-neighbor sites in odd-$N$-site systems, whereas localization can be significantly enhanced by SOC in even-$N$-site systems. More interestingly, it is found destruction and revival of CDT observable in non-high-frequency regimes. Our results can be readily verified within the capacity of current experiments.

Coherent Destruction of Tunneling of Bosons with Effective Three-Body Interactions* *Supported by the National Natural Science Foundation of China under Grant Nos. 11274255 and 11305132, Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20136203110001, the Natural Science Foundation of Gansu Province under Grant No. 2011GS04358, and Creation of Science and Technology of Northwest

The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically. In our findings, when the system is with only repulsive two-body interactions or only three-body interactions, the tunneling will be suppressed; while in the case of the coupling between two- and three-body interactions, the tunneling can be either suppressed or enhanced. Particularly, when attractive three-body interactions are twice large as repulsive two-body interactions, CDT occurs at isolated points of driving force, which is similar to the linear case. Considering different interaction, the system can experience different transformation from coherent tunneling to coherent destruction of tunneling (CDT). The quasi-energy of the system as the function of the periodically driving force shows a triangular structure, which provides a deep insight into the tunneling dynamics of the system.

Controlling the Directed Quantum Transport of Ultracold Atoms in an Optical Lattice with a Periodic Driving Field

We propose a new method to control the directed quantum transport of ultracold atoms in a one-dimensional optical lattice. In this proposal, the effective tunneling between the neighboring sites can be adjusted via coherent destruction of tunneling by tuning the phase of the external field, instead of using the driving field intensity or the frequency, thus the directed quantum transport of ultracold atoms can be coherently controlled in a much easier manner. Our proposal overcomes the major drawback of the method used by Creffield et al. [Phys. Rev. Lett. 99 (2007) 110501], and can be implemented, in principle, in any one-dimensional optical lattice. Some potential applications of the scheme are also discussed.

Dynamical effects of counter-rotating couplings on interference between driving and dissipation

We use an analytical method to study the dissipative dynamics of a two-level system (TLS) under a harmonic driving. The method is based on a combination of the unitary transformation and Born--Markov master-equation approach. Our main aim is to clarify the effects of counter-rotating (CR) terms of both the driving and TLS-bath (dissipative) coupling on the dynamics, in comparison with the rotating-wave results of different schemes, i.e., the well-known traditional rotating-wave approximation method, and two particular methods: one just takes into account the effects of the driving CR terms and the other the effects of the dissipative CR terms, which are derived from our general treatment. Our main results are as follows: (i) by calculating the time-dependent population difference and coherence, in the case of resonant strong driving, we demonstrate that the CR terms of both the driving and dissipative coupling play an important role in the relaxation and dephasing processes, and also the properties of the steady state; (ii) in the case of largely detuned driving, we find that the CR terms of the dissipative coupling become negligible while those of the driving contribute dominant modifications to the time evolution and steady state. Moreover, we examine the influence of the dissipation on coherent destruction of tunneling under a largely detuned strong driving. We show that an almost complete suppression of the tunneling can be achieved for a relatively long time; (iii) under certain conditions, we find numerical equivalence between one of two particular methods and the Floquet--Born--Markov approach based on exact numerical treatment of the Floquet Hamiltonian. It turns out that our method is more simple and efficient than the Floquet--Born--Markov approach for both analytical and numerical calculations. By the general comparison of different treatments we demonstrate the dynamical effects of CR terms of both the driving and the dissipative coupling on the coherence and population difference.