We propose a time-domain "interferometer" based on ultracold Bose atoms loaded on a double well potential. By the adiabatic Rosen-Zener process, the barrier between two wells is ramped down slowly, held for a while, then ramped back. Starting with a coherent state of double well system, the final occupations on one well show interesting interference fringes in the time-domain. The fringe pattern is sensitive to the initial state, the interatomic interaction, and the external forces such as gravity which can change the shape of the double well. In this sense, this interferometric scheme has the potentials for precision measurements with ultracold atoms. The underlying mechanism is revealed and possible applications are discussed.
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 perform Landau-Zener-Stuckelberg interferometry on a single electron GaAs charge qubit by repeatedly driving the system through an avoided crossing. We observe coherent destruction of tunneling, where periodic driving with specific amplitudes inhibits current flow. We probe the quantum dot occupation using a charge sensor, observing oscillations in the qubit population resulting from the microwave driving. At a frequency of 9 GHz we observe excitation processes driven by the absorption of up to 17 photons. Simulations of the qubit occupancy are in good agreement with the experimental data.
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…
Controlling coherent interaction at avoided crossings is at the heart of quantum information processing. The regime between sudden switches and adiabatic transitions is characterized by quantum superpositions that enable interference experiments. Here, we implement periodic passages at intermediate speed in a GaAs-based two-electron charge qubit and observe Landau-Zener-Stückelberg-Majorana (LZSM) quantum interference of the resulting superposition state. We demonstrate that LZSM interferometry is a viable and very general tool to not only study qubit properties but beyond to decipher decohere…
We study Rosen-Zener transition (RZT) in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. We find that the nonlinearity could affect the quantum transition dramatically. At certain nonlinearity the 100% population transfer between two levels is observed and found to be robust over a very wide range of external parameters. On the other hand, the quantum transition could be completely blocked by a strong nonlinearity. In the sudden and adiabatic limits we have derived analytical e…
Using the Landau-Zener-Stückelberg-Majorana-type (LZSM) semiclassical approach, we study both graphene and a thin film of a Weyl semimetal subjected to a strong AC electromagnetic field. The spectrum of quasi energies in the Weyl semimetal turns out to be similar to that of a graphene sheet. Earlier it has been predicted qualitatively that the transport properties of strongly-irradiated graphene oscillate as a function of the radiation intensity [S.V. Syzranov et al., Phys. Rev. B 88, 241112 (2013)]. Here we obtain rigorous quantitative results for a driven linear conductance of graphene and a…
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 perform Landau-Zener-Stuckelberg-Majorana (LZSM) spectroscopy on a system with strong spin-orbit interaction (SOI), realized as a single hole confined in a gated double quantum dot. In analogy to the electron systems, at magnetic field B=0 and high modulation frequencies we observe the photon-assisted tunneling (PAT) between dots, which smoothly evolves into the typical LZSM funnel-shaped interference pattern as the frequency is decreased. In contrast to electrons, the SOI enables an additional, efficient spin-flipping interdot tunneling channel, introducing a distinct interference pattern …
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…
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 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 distinguish different mechanisms for population inversion in flux qubits driven by dc+ac magnetic fields. We show that for driving amplitudes such that there are Landau-Zener-Stückelberg intereferences, it is possible to have population inversion solely mediated by the environmental bath at long driving times. We study the effect of the resonant frequency $Ω_p$ of the measuring circuit, finding different regimes for the asymptotic population of the state of the flux qubit. By tailoring $Ω_p$ the degree of population inversion can be controlled. Our studies are based on realistic simulations…
We investigate the Landau-Zener-Stuckelberg-Majorana interferometry of a superconducting qubit in a semi-infinite transmission line terminated by a mirror. The transmon-type qubit is at the node of the resonant electromagnetic (EM) field, hiding from the EM field. "Mirror, mirror" briefly describes this system, because the qubit acts as another mirror. We modulate the resonant frequency of the qubit by applying a sinusoidal flux pump. We probe the spectroscopy by measuring the reflection coefficient of a weak probe in the system. Remarkable interference patterns emerge in the spectrum, which c…
In this work we propose a way to unveil the type of environmental noise in strongly driven superconducting flux qubits through the analysis of the Landau-Zener-Stückelberg (LZS) interferometry. We study both the two-level and the multilevel dynamics of the flux qubit driven by a dc+ac magnetic field. We found that the LZS interference patterns exhibit well defined multiphoton resonances whose shape strongly depend on the time scale and the type of coupling to a quantum bath. For the case of transverse system-bath coupling, the n-photon resonances are narrow and nearly symmetric with respect to…
We consider a general theory of Landau-Zener transitions in a three-level system. Based on a classification of three level crossings we express the Landau - Zener Hamiltonians in terms of two bases: i) spin S=1 SU(2) operators and ii) SU(3) Gell - Mann matrices. We show that the generic Hamiltonians being non-linear in terms of the SU(2) group generators become linear in the SU(3) basis. If the diabatic states of the SU(3) Landau - Zener Hamiltonian form a triangle, the interference between two paths results in formation of "beats" and "steps" pattern in the time-dependent transition probabili…
The implementation of quantum technologies in electronics leads naturally to the concept of coherent single-electron circuits, in which a single charge is used coherently to provide enhanced performance. In this work, we propose a coherent single-electron device that operates as an electrically-tunable capacitor. This system exhibits a sinusoidal dependence of the capacitance with voltage, in which the amplitude of the capacitance changes and the voltage period can be tuned by electric means. The device concept is based on double-passage Landau-Zener-Stückelberg-Majorana interferometry of a co…
We study Landau-Zener-Stückelberg (LZS) interferometry in a cQED architecture under effects of dissipation. To be specific, we consider a superconducting qubit driven by a dc+ac signal and coupled to a transmission line resonator, but our results are valid for general qubit-resonators devices. To take the environment into account, we assume that the resonator is coupled to an ohmic quantum bath. The Floquet-Born-Markov master equation is numerically solved to obtain the dynamics of the system for arbitrary amplitude of the drive and different time scales. We unveil important differences in the…
Schrödinger cat states are useful for many applications, ranging from quantum information processing to high-precision measurements. In this paper we propose a conceptually new method for creating such cat states, based on photon-assisted Landau-Zener-Stückelberg interferometry in a hybrid system consisting of a qubit coupled to a photon cavity. We show that by initializing the qubit in one of its basis states, performing three consecutive sweeps of the qubit energy splitting across the 1-photon resonance, and finally projecting the qubit to the same basis state, the parity of the photon field…
Stimulated by a very recent experiment observing successfully two superconducting states with even- and odd-number of electrons in a nanowire topological superconductor as expected from the existence of two end Majorana quasiparticles (MQs) [Albrecht \textit{et al.}, Nature \textbf{531}, 206 (2016)], we propose a way to manipulate Majorana qubit exploiting quantum tunneling effects. The prototype setup consists of two one-dimensional (1D) topological superconductors coupled by a tunneling junction which can be controlled by gate voltage. We show that, upon current injection, the time evolution…
We develop the Landau-Zener transfer matrix theory for the instantaneous Floquet states (IFSs) for quantum systems driven by strong pulse lasers. Applying this theory to the pulse excitation probability in two-level quantum systems, we show unexpectedly good quantitative agreements for few-cycle pulses. This approach enables us to qualitatively understand the probability's peculiar behaviors as quantum path interference between IFSs. We also study the pulse-width dependence, finding that this Floquet-state interpretation remains useful for shorter pulses down to 2-cycle ones in the present mod…
We study Landau-Zener-Stuckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from a LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also sho…
Single spin state evolution induced by the Landau-Zener-Stückelberg-Majorana (LZSM) interference in a Zeeman-spit four level system in a periodically driven double quantum dot is studied theoretically by the Floquet stroboscopic method. An interplay between spin-conserving and spin-flip tunneling processes with the Electric Dipole Spin Resonance (EDSR) that is induced in an individual dot and enhanced by the LZSM multiple level crossings with the neighboring quantum dot is investigated as a function of the microwave (MW) frequency, driving amplitude, interdot detuning, and magnetic field. A nu…
Recent experiments have shown that Landau-Majorana-Stuckelberg-Zener (LMSZ) interferometry is a powerful tool for demonstrating and exploiting quantum coherence not only in atomic systems but also in a variety of solid state quantum systems such as spins in quantum dots, superconducting qubits, and nitrogen vacancy centers in diamond. In this work, we propose and develop a general (and, in principle, exact) theoretical formalism to identify and characterize the interference resonances that are the hallmark of LMSZ interferometry. Unlike earlier approaches, our scheme does not require any appr…
Coupled nanomechanical resonators have recently attracted much attention for both fundamental studies in physics and broad applications in high-precession detection or sensing. By studying the Landau-Zener transitions and Rabi oscillation of two coupled resonators, it has been shown that such a two-mode system acts as a classical two-level system bearing the analog to a quantum mechanical two-level one. Here we construct a Stückelberg interferometer with two coupled cantilevers by driving the system through the avoided crossing twice. By measuring the non-adiabatic phase acquired at the Landau…
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…
The electron momentum density obtained from the Schwinger-like mechanism is evaluated for a graphene sample immersed in a homogeneous time-dependent electric field. Based on the analogy between graphene low-energy electrons and quantum electrodynamics (QED), numerical techniques borrowed from strong field QED are employed and compared to approximate analytical approaches. It is demonstrated that for some range of experimentally accessible parameters, the pair production proceeds by sequences of adiabatic evolutions followed by non-adiabatic Landau-Zener transitions, reminiscent of the Kibble-Z…
