We study the interband Landau-Zener tunneling of a quantum particle in the Hall configuration, i.e., in the presence of normal to the lattice plane gauge field (for example, magnetic field for a charged particle) and in-plane potential field (electric field for a charged particle). The interband tunneling is induced by the potential field and for vanishing gauge field is described by the common Landau-Zener theory. We generalize this theory for non-zero gauge field. The depletion rates of low-energy bands are calculated by using semi-analytical method of the truncated Floquet matrix.
We present a method to perform fault-tolerant single-qubit gate operations using Landau-Zener tunneling. In a single Landau-Zener pulse, the qubit transition frequency is varied in time so that it passes through the frequency of the radiation field. We show that a simple three-pulse sequence allows eliminating errors in the gate up to the third order in errors in the qubit energies or the radiation frequency.
We calculate the exact Landau-Zener transitions probabilities for a qubit with arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of a diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.
Under resonant conditions, a long sequence of landau-zener transitions can lead to Rabi oscillations. Using a nitrogen-vacancy (NV) center spin in diamond, we investigated the interference between more than 100 Landau-Zener processes. We observed the new type of Rabi oscillations of the electron spin resulting from the interference between successive Landau-Zener processes in various regimes, including both slow and fast passages. The combination of the control techniques and the favorable coherent properties of NV centers provides an excellent experimental platform to study a variety of quant…
We demonstrate quantum control and entanglement generation using a Landau-Zener beam splitter formed by coupling two transmon qubits to a superconducting cavity. Single passage through the cavity-mediated qubit-qubit avoided crossing provides a direct test of the Landau-Zener transition formula. Consecutive sweeps result in Landau-Zener-Stuckelberg interference patterns, with a visibility that can be sensitively tuned by adjusting the level velocity through both the non-adiabatic and adiabatic regimes. Two-qubit state tomography indicates that a Bell state can be generated via a single passage…
I present a simple algorithm based on a type of partial reverse-engineering that generates an unlimited number of exact analytical solutions to the Schrodinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this method by deriving new exact solutions corresponding to fast control pulses that contain arbitrarily many tunable parameters. It is shown that the formalism is naturally suited to generating analytical control protocols that perform precise non-adiabatic rapid passage and Landau-Zener interferometry near the quantum speed limit. A general, exact formula for …
We study the S-matrix for the transitions at an avoided crossing of several energy levels, which is a multilevel generalization of the Landau-Zener problem. We demonstrate that, by extending the Schroedinger evolution to complex time, one can obtain an exact answer for some of the transition amplitudes. Similar to the Landau-Zener case, our result covers both the adiabatic regime (slow evolution.) and the diabatic regime (fast evolution). The form of the exact transition amplitude coincides with that obtained in a sequential pairwise level crossing approximation, in accord with the conjecture …
We analyze dynamics of a quantum particle in a square lattice in the Hall configuration beyond the single-band approximation. For vanishing gauge (magnetic) field this dynamics is defined by the inter-band Landau-Zener tunneling, which is responsible for the phenomenon known as the electric breakdown. We show that in the presence of a gauge field this phenomenon is absent, at least, in its common sense. Instead, the Landau-Zener tunneling leads to appearance of a finite current which flows in the direction orthogonal to the vector of a potential (electric) field.
Since the pioneering works by Landau, Zener, Stückelberg, and Majorana (LZSM), it has been known that driving a quantum two-level system results in tunneling between its states. Even though the interference between these transitions is known to be important, it is only recently that it became both accessible, controllable, and useful for engineering quantum systems. Here, we study systematically various aspects of LZSM physics and review the relevant literature, significantly expanding the review article in [Shevchenko, S. N., S. Ashhab, and F. Nori (2010), "Landau-Zener-Stückelberg interferom…
We study Landau-Zener dynamics in a double quantum dot filled with two electrons, where the spin states can become correlated with charge states and the level velocity can be tuned in a time-dependent fashion. We show that a correct interpretation of experimental data is only possible when finite-time effects are taken into account. In addition, our formalism allows the study of partial adiabatic dynamics in the presence of phonon-mediated hyperfine relaxation and charge-noise-induced dephasing. Our findings demonstrate that charge noise severely impacts the visibility of Landau-Zener-Stückelb…
We present a derivation of the Landau-Zener solution through the explicit evaluation of the time ordered propagator. The result is exact and does not involve the solution of the differential equation for the spin amplitudes.
For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, to survive the transition and to remain in the first level, does not depend on whether or not the second level is broadened [V. M. Akulin and W. P. Schleicht, Phys. Rev. A {\bf 46}, 4110 (1992)]. In other words, the seminal Landau-Zener result applies regardless of the broadening of the second level. The same question for the multistate Landau-Zener transition is addressed in the present paper. While for integrable multistate models, where the transition does not involve interfere…
We monitor the Landau-Zener dynamics of a single-ion magnet in a spin-transistor geometry. For increasing field-sweep rates, the spin reversal probability shows increasing deviations from that of a closed system. In the low-conductance limit, such deviations are shown to result from a dephasing process. In particular, the observed behaviors are succesfully simulated by means of an adiabatic master equation, with time averaged dephasing (Lindblad) operators. The time average is tentatively interpeted in terms of the finite time resolution of the continuous measurement.
We irradiated an rf-SQUID qubit with large-amplitude and high frequency electromagnetic field. Population transitions between macroscopic distinctive quantum states due to Landau-Zener transitions at energy-level avoided crossings were observed. The qubit population on the excited states as a function of flux detuning and microwave power exhibits interference patterns. Some novel features are found in the interference and a model based on rate equations can well address the features.
We investigate the influence of temperature and dissipation on the Landau-Zener transition probability in circuit QED. Dissipation is modelled by coupling the transmission line to a bath of harmonic oscillators. The reduced description for the density operator is treated within Bloch-Redfield theory. A phase-space representation allows an efficient numerical implementation of the resulting master equation. It provides reliable results which are valid even for rather low temperatures. We find that the spin-flip probability as a function of temperature and dissipation strength exhibits a non-mon…
We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-Stückelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that pr…
A quantum system can be driven by either sinusoidal, rectangular, or noisy signals. In the literature, these regimes are referred to as Landau-Zener-Stuckelberg-Majorana (LZSM) interferometry, latching modulation, and motional averaging, respectively. We demonstrate that these pronounced and interesting effects are also inherent in the dynamics of classical two-state systems. We discuss how such classical systems are realized using either mechanical, electrical, or optical resonators. In addition to the fundamental interest of such dynamical phenomena linking classical and quantum physics, we …
We identify a nontrivial 4-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical pictu…
We report an experimental measurement of Landau-Zener transitions on an individual flux qubit within a multi-qubit superconducting chip designed for adiabatic quantum computation. The method used isolates a single qubit, tunes its tunneling amplitude Delta into the limit where Delta is much less than both the temperature T and the decoherence-induced energy level broadening, and forces it to undergo a Landau-Zener transition. We find that the behavior of the qubit agrees to a high degree of accuracy with theoretical predictions for Landau-Zener transition probabilities for a double-well quantu…
We study a qubit undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the qubit, being independent of the frequency of the QED mode. Possible applications are single-photon generation and the controllable creation of qubit-oscillator entanglement.
We generalize the Landau-Zener theory of coherent tunneling transitions by taking thermal relaxation into account. The evaluation of a new generalized master equation containing a dynamic tunneling rate that includes the interaction between the relevant system and its environment leads to an incoherent Zener transition probability with an exponent that is twice as large as the one of the coherent Zener probability in the limit T -> 0. We apply our results to molecular clusters, in particular to recent measurements of the tunneling transition of spins in Fe8 crystals performed by Wernsdorfer an…
We investigate optical Bloch oscillation, Zener tunneling and breathing modes in arrays of optical waveguides. We perform a new method of calculation based on the multiple scattering formalism. To demonstrate Bloch oscillation and breathing modes, we consider a planar array of parallel cylindrical waveguides with the refractive index gradually varying across the array. We demonstrate that the form of Bloch oscillation may be predicted by means of dispersion law analysis. To demonstrate Zener tunneling, we consider a planar array of cylindrical waveguides of two types situated by turn. The band…
Application of strong dc electric field to an insulator leads to quantum tunneling of electrons from the valence band to the conduction band, which is a famous nonlinear response known as Landau-Zener tunneling. One of the growing interests in recent studies of nonlinear responses is nonreciprocal phenomena where transport toward the left and the right differs. Here, we theoretically study Landau-Zener tunneling in noncentrosymmetric systems, i.e., the crystals without spatial inversion symmetry. A generalized Landau-Zener formula is derived taking into account the geometric nature of the wave…
An innovative microscopic model with a minimal number of parameters: tunneling splitting gap, external field sweeping velocity, and decoherence rate is used to describe dynamics of the dissipative Landau-Zener transition in the presence of the decoherence. In limiting cases, the derived equation of motion gives rise to the well-known Landau-Zener and Kayanuma formula. In a general case, the description demonstrates a non-monotonic flipping probability with respect to the sweeping velocity, which is also found in some other models. This non-monotony can be explained by considering the competiti…
A simple mechanical analog describing Landau-Zener tunneling effect is proposed using two weakly coupled chains of nonlinear oscillators with gradually decreasing (first chain) and increasing (second chain) masses. The model allows to investigate nonlinear generalization of Landau-Zener tunneling effect considering soliton propagation and tunneling between the chains. It is shown that soliton tunneling characteristics become drastically dependent on its amplitude in nonlinear regime. The validity of the developed tunneling theory is justified via comparison with direct numerical simulations on…
We study the influence of a fast noise on Landau-Zener transitions. We demonstrate that a fast colored noise much weaker than the conventional white noise can produce transitions itself or can change substantially the Landau-Zener transition probabilities. In the limit of fast colored or strong white noise we derive asymptotically exact formulae for transition probabilities and study the time evolution of a spin coupled to the noise and a sweeping magnetic field.
We propose a simple ansatz that allows to generate new exactly solvable multi-state Landau-Zener models. It is based on a system of two decoupled two-level atoms whose levels vary with time and cross at some moments. Then we consider multiparticle systems with Heisenberg equations for annihilation operators having similar structure with Shrödinger equation for amplitudes in multistate Landau-Zener models and show that the corresponding Shrödinger equation in multiparticle sector belongs to the multistate Landau-Zener class. This observation allows to generate new exactly solvable models from a…
Quantum-mechanical systems having two discrete energy levels are ubiquitous in nature. For crossing energy levels, depending on how fast they approach each other, there is a possibility of a transition between them. This phenomenon is known as Landau-Zener tunneling and it forms the physical basis of the Zener diode, for example. The traditional treatment of the Landau-Zener tunneling, however, ignores quantum-mechanical interference. Here we report an observation of phase-sensitive interference between consecutive Landau-Zener tunneling attempts in an artificial two-level system formed by a C…
We present an exact asymptotic solution for electron transition amplitudes in an infinite linear chain driven by an external homogeneous time-dependent electric field. This solution extends the Landau-Zener theory for the case of infinite number of states in discrete spectrum. In addition to transition amplitudes we calculate an effective diffusion constant.
Motivated by recent realizations of qubits with a readout by macroscopic quantum tunneling in a Josephson junction, we study the problem of barrier penetration in presence of coupling to a spin-${1\over 2}$ system. It is shown that when the diabatic potentials for fixed spin intersect in the barrier region, Landau- -Zener transitions lead to an enhancement of the tunneling rate. The effect of these spin flips in imaginary time is in qualitative agreement with experimental observations.
We study the Landau-Zener tunneling problem for particles bound in periodic lattice insulators. To this end, we construct the path integral based on the Bloch and Wannier functions in the presence with an external force, and the transition amplitude is calculated for the Su-Schrieffer-Heeger model. We find that the tunneling probability in bulk periodic systems becomes drastically larger than that by the Landau-Zener formula. This enhancement is prominent for small values of the external field or small hopping integral compared with the gap, and comes from the difference between the Dirac and …
The Landau Zener method allows to measure very small tunnel splittings Δin molecular clusters Fe_8. The observed oscillations of Δas a function of the magnetic field applied along the hard anisotropy axis are explained in terms of topological quantum interference of two tunnel paths of opposite windings. Studies of the temperature dependence of the Landau Zener transition rate P gives access to the topological quantum interference between exited spin levels. The influence of nuclear spins is demonstrated by comparing P of the standard Fe_8 sample with two isotopically substituted samples. The …
We formulate and approximately solve a specific many-body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving rates. The structure of the theory suggests that this finding reflects a more general phenomenon in the physics of adiabatically driven many particle systems. Our solution can be used to understand, for example, the behavior of two-level systems coupled to an electromagnetic field, as realized in cavity QED experiments.
We identify a nontrivial multistate Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the Landau-Zener formula. We discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matri…
Optomechanical systems couple light to the motion of nanomechanical objects. Intriguing new effects are observed in recent experiments that involve the dynamics of more than one optical mode. There, mechanical motion can stimulate strongly driven multi-mode photon dynamics that acts back on the mechanics via radiation forces. We show that even for two optical modes Landau-Zener-Stueckelberg oscillations of the light field drastically change the nonlinear attractor diagram of the resulting phonon lasing oscillations. Our findings illustrate the generic effects of Landau-Zener physics on back-ac…
By driving a 3D transmon with microwave fields, we generate an effective avoided energy-level crossing. Then we chirp microwave frequency, which is equivalent to driving the system through the avoided energy-level crossing by sweeping the avoided crossing. A double-passage chirp produces Landau-Zener-Stückelberg-Majorana interference that agree well with the numerical results. Our method is fully applicable to other quantum systems that contain no intrinsic avoided level crossing, providing an alternative approach for quantum control and quantum simulation.
A Zener diode is a paradigmatic device in semiconductor-based electronics that consists of a pn junction where an external electric field induces a switching behavior in the current-voltage characteristics. We study Zener tunneling in HgTe quantum wells and graphene multilayers. We find that the tunneling transition probability depends asymmetrically on the parallel momentum of the carriers to the barrier. In HgTe quantum wells the asymmetry is the opposite for each spin, whereas for graphene multilayers it is the opposite for each valley degree of freedom. In both cases, a spin/valley current…
In a recent Letter [S. Ganeshan, E. Barnes, and S. Das Sarma, Phys. Rev. Lett. 111, 130405 (2013)], Ganeshan et al. present a general framework to classify the resonance structure of Landau-Majorana-Stuckelberg-Zener interferometry into three basic categories distinguished by whether these resonances correspond to periodic or nonperiodic quantum evolution. In this Comment, we show that their identification of the real resonances in the regime of small drive amplitude is incorrect.
We obtain the exact expression for the matrix of nonadiabatic transition probabilities in the model of three interacting states with a time-dependent Hamiltonian. Unlike other known solvable Landau-Zener-like problems, our solution is generally expressed in terms of hypergeometric functions that have relatively complex behavior, e.g. the obtained transition probabilities may show multiple oscillations as functions of parameters of the model Hamiltonian.
The large tunneling anisotropic magneto-resistance of a single $p^{++}$-(Ga,Mn)As/$n^{+}$-GaAs Zener-Esaki diode is evidenced in a perpendicular magnetic field over a large temperature and voltage range. Under an applied bias, the tunnel junction transparency is modified, allowing to continuously tune anisotropic transport properties between the tunneling and the ohmic regimes. Furthermore, an asymmetric bias-dependence of the anisotropic tunneling magneto-resistance is also observed: a reverse bias highlights the full (Ga,Mn)As valence band states contribution, whereas a forward bias only pro…
The Landau-Zener transition in a two level system can be suppressed or enhanced by coupling to an environment, depending on the temperature and the environment spectral function. We consider the marginal spectral function, when the dissipation effects are important for arbitrarily slow motion. Landau-Zener transition rate demonstrates a non-trivial dependence of the on the ``bias'', i. e. on the rate of the two energy levels relative motion. The Landau-Zener transition is fully suppressed for the values of the bias below a threshold bias set by the coupling strength. Above the threshold, the t…
We report a theoretical/experimental study of current-voltage characteristics (I-V) of graphene devices near the Dirac point. The I-V can be described by a power law (I \propto V^α, with 1< α<= 1.5). The exponent is higher when the mobility is lower. This superlinear I-V is interpreted in terms of the interplay between Zener-Klein transport, that is tunneling between different energy bands, and defect scattering. Surprisingly, the Zener-Klein tunneling is made visible by the presence of defects.
We consider the transition of electron between two quantum dots in which the discrete levels are swept past each other with a constant velocity. If a direct tunneling between the dot levels was allowed, an electron will be transferred between the dots when the levels cross. This transfer is described in terms of the conventional Landau-Zener theory. We assume that direct tunneling between the dots is forbidden. Rather, the transfer is due to the resonant tunneling via a discrete impurity level separating the dots. Then the description of the electron transfer reduces to a threestate (two dots …
We report strong light emission from a room-temperature n-type unipolar-doped In0.53Ga0.47As/AlAs double-barrier resonant-tunneling diode (DBRTD) precisely at the In0.53Ga0.47As band-edge near 1650 nm. The emission characteristics are very similar to what was observed recently in GaN/AlN DBRTDs, both of which suggest that the mechanism for emission is cross-gap electron-hole recombination via resonant- and Zener co-tunneling of electrons, the latter mechanism generating the required holes. Analysis shows that because of the relatively small bandgap, the Zener tunneling probability can be large…
We propose a new type of interferometry, based on geometric phases accumulated by a periodically driven two-level system undergoing multiple Landau-Zener transitions. As a specific example, we study its implementation in a superconducting charge pump. We find that interference patterns appear as a function of the pumping frequency and the phase bias, and clearly manifest themselves in the pumped charge. We also show that the effects described should persist in the presence of realistic decoherence.
We have investigated tunneling current through a suspended graphene Corbino disk in high magnetic fields at the Dirac point, i.e. at filling factor $ν$ = 0. At the onset of the dielectric breakdown the current through the disk grows exponentially before ohmic behaviour, but in a manner distinct from thermal activation. We find that Zener tunneling between Landau sublevels dominates, facilitated by tilting of the source-drain bias potential. According to our analytic modelling, the Zener tunneling is strongly affected by the gyrotropic force (Lorentz force) due to the high magnetic field
We study generation and dynamics of an exchange spin qubit encoded in three coherently coupled quantum dots with three electrons. For two geometries of the system a linear and a triangular one, the creation and coherent control of the qubit states are performed by the Landau--Zener transitions. In the triangular case both the qubit states are equivalent and can be easily generated for particular symmetries of the system. If one of the dots is smaller than the others one can observe Rabi oscillations, that can be used for coherent manipulation of the qubit states. The linear system is easier to…
Temperature-independent magnetic viscosity in ferritin has been observed from 2 K down to 100 mK, proving that quantum tunneling plays the main role in these particles at low temperature. Magnetic relaxation has also been studied using the Landau-Zener method making the system crossing zero resonant field at different rates, alpha=dH/dt, ranging from 10^{-5} to 10^{-3} T/s, and at different temperatures, from 150 mK up to the blocking temperature. We propose a new Tln(Delta H_{eff}/tau_0 alpha) scaling law for the Landau-Zener probability in a system distributed in volumes, where Delta H_{eff}…
We study theoretically the impact of Zener tunneling on the charge-transport properties of quasi-metallic (Qm) carbon nanotubes (characterized by forbidden band gaps of few tens of meV). We also analyze the interplay between Zener tunneling and elastic scattering on defects. To this purpose we use a model based on the master equation for the density matrix, that takes into account the inter-band Zener transitions induced by the electric field (a quantum mechanical effect), the electron-defect scattering and the electron-phonon scattering. In presence of Zener tunnelling the Qm tubes support an…
We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ) transitions leads to co-flips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.
The spin-dependent electron transport has been studied in magnetic semiconductor waveguides (nanowires) in the helical magnetic field. We have shown that -- apart from the known conductance dip located at the magnetic field equal to the helical-field amplitude $B_h$ -- the additional conductance dips (with zero conductance) appear at magnetic field different from $B_h$. This effect occuring in the non-adiabatic regime is explained as resulting from the resonant Landau-Zener transitions between the spin-splitted subbands.
We investigate the ballistic zitterbewegung dynamics and the Landau-Zener tunneling between edge and bulk states of wave packets in two-dimensional topological insulators. In bulk, we use the Ehrenfest theorem to show that an external in-plane electric field not only drifts the packet longitudinally, but also induces a transverse finite side-jump for both trivial and topological regimes. For finite ribbons of width $W$, we show that the Landau-Zener tunneling between bulk and edge states vanishes for large $W$ as their electric field-induced coupling decays with $W^{-3/2}$. This is demonstrate…
We study Landau-Zener transitions between two states with the addition of a shared discretized continuum. The continuum allows for population decay from the initial state as well as indirect transitions between the two states. The probability of nonadiabatic transition in this multichannel model preserves the standard Landau-Zener functional form except for a shift in the usual exponential factor, reflecting population transfer into the continuum. We provide an intuitive explanation for this behavior assuming independent individual transitions between pairs of states. In contrast, the probabil…
We show that the probability of electric field induced interband tunneling in solid state systems is generically a non-monotonic (oscillatory) function of the applied field. This unexpected behavior can be understood as arising due to a common path interference between two distinct tunneling solutions. The phenomenon is insensitive to magnetic field, and arises whenever the low energy dispersion relation contains higher order terms in addition to the usual $p^2$ term. Such higher order terms are generically present, albeit with small co-efficient, so that the oscillatory Zener tunneling is a u…
We develop a comprehensive, elegant theory to explain terahertz (THz) emission from a superlattice over a wide range of applied electric field,which shows excellent agreement between theory andexperiment for a GaAs/Al{0.3}Ga{0.7As superlattice. Specifically we show that increasing electric field increases THz emission for low fields, then reduces emission for medium fields due to field-induced wave function localization, and then increases emission in the high field due to delocalization and Zener tunneling between minibands. Our theory shows that Zener tunneling resonances yield high THz emis…
We consider an adiabatic Landau-Zener model of two-level system diagonally coupled to an Ohmic bosonic bath of large spectral width and derive through fermionization its exact solution at a special value of the coupling constant. From this solution we obtain the characteristic function of the distribution of energy transferred to the bath during the evolution of the system ground state as a functional determinant of a single particle operator. At zero temperature this distribution is further found to be exponential and at finite temperature the first three moments of the distribution are calcu…
Multitime Landau-Zener (MTLZ) model is a class of exactly solvable quantum many-body models which is multitstate and multitime generalization of the two-state Landau-Zener model. Currently discovered MTLZ models include the "hypercubes", the "fans" and their direct product models. In this work, we prove two no-go rules, named the "no $K_{3,3}$" rule and the "no $1221$" rule, which forbid the existence of exact solutions for models with certain structures of interactions. We further apply these rules to show that for models with no more than $9$ states, besides the models mentioned above there …
We study the Landau-Zener dynamics of a tunneling spin coupled to a torsional resonator. For strong spin-phonon coupling, when the oscillator frequency is large compared to the tunnel splitting, the system exhibits multiple Landau-Zener transitions. Entanglement of spin and mechanical angular momentum results in abrupt changes of oscillator dynamics which coincide in time with spin transitions. We show that a large number of spins on a single oscillator coupled only through the in-phase phonon field behaves as a single large spin, greatly enhancing the spin-phonon coupling. We compare purely q…
We show by direct calculation starting from a microscopic model that the two-state system with time-dependent energy levels in the presence of fast quantum noise obeys the master equation. The solution of master equation is found analytically and analyzed in a broad range of parameters. The fast transverse noise affects the transition probability during much longer time (the accumulation time) than the longitudinal one. The action of the fast longitudinal noise is restricted by the shorter Landau-Zener time, the same as in the regular Landau-Zener process. The large ratio of time scales allows…
A qubit may undergo Landau-Zener transitions due to its coupling to one or several quantum harmonic oscillators. We show that for a qubit coupled to one oscillator, Landau-Zener transitions can be used for single-photon generation and for the controllable creation of qubit-oscillator entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a qubit coupled to two cavities, we show that Landau-Zener sweeps of the qubit are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the qubit acting as the entanglement…
