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 resonant patterns between the Strong Coupling and Ultra Strong Coupling regimes in the qubit-resonator interaction, which are mainly due to the magnitude of photonic gaps in the energy spectrum of the system. We identify in the LZS patterns the contribution of the qubit gap and the photonic gaps, showing that for large driving amplitudes the patterns present a weaving structure due to the combined intercrossing of the different gaps contributions.
Controllable single spin evolution at sub-harmonics of electric dipole spin resonance enhanced by four-level Landau-Zener-St{ü}ckelberg-Majorana interference
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 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 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…
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 demonstrate quantum coherent control of a single electron spin in a NV center in diamond using the Landau-Zener-Stuckelberg interferometry at room temperature. Interference pattern is observed oscillating as a function of microwave frequency. The decays in the visibility of the interference are well explained by numerical simulation which includes the thermal fluctuations of the nuclear bath which shows that Landau-Zener-Stuckelberg interferometry can be used for probing electron spin decoherence processes.
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…
Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. In this Letter, we combine these two approaches to study the dynamics of a superconducting phase qubit. We experimentally demonstrate Landau-Zener interferometry based on the pure geometric phases in this solid-state qubit. We observe the interference caused by a pure geometric phase accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is canceled out by a spin-echo pulse. The full controllability of the qubit state as a funct…
We report the first experimental realization of the geometric Landau-Zener-Stückelberg (LZS) interferometry proposed by [Phys. Rev. Lett. 107, 207002 (2011)] in a single trapped ion system. Different from a conventional LZS interferometer, the interference fringes of our geometric interferometer originate solely from geometric phase. We also observe the robustness of the interference contrast against noise or fluctuation in the experimental parameters. Our scheme can be applied to other complex systems subject to relatively large errors in system control.
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…
Employing the time-dependent variational principle combined with the multiple Davydov $\mathrm{D}_2$ Ansatz, we investigate Landau-Zener (LZ) transitions in a qubit coupled to a photon mode with various initial photon states at zero temperature. Thanks to the multiple Davydov trial states, exact photonic dynamics taking place in the course of the LZ transition is also studied efficiently. With the qubit driven by a linear external field and the photon mode initialized with Schrödinger-cat states, asymptotic behavior of the transition probability beyond the rotating-wave approximation is uncove…
We systematically investigate the non-Hermitian generalisations of the Landau-Zener (LZ) transition and the Landau-Zener-Stückelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behaviour analysed. We then focus on non-Hermitian systems with a real adiabatic parameter and study the LZS interferometry formed out of two identical avoided level crossings. Four distinctive cases of interferometry are identified and the analytic formulae for the transition probabilities are calculated for each case.…
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 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…
A transition between energy levels at an avoided crossing is known as a Landau-Zener transition. When a two-level system (TLS) is subject to periodic driving with sufficiently large amplitude, a sequence of transitions occurs. The phase accumulated between transitions (commonly known as the Stuckelberg phase) may result in constructive or destructive interference. Accordingly, the physical observables of the system exhibit periodic dependence on the various system parameters. This phenomenon is often referred to as Landau-Zener-Stuckelberg (LZS) interferometry. Phenomena related to LZS interfe…
Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and…
We analyze the dynamics of a two-level quantum system (TLS) under the influence of a strong sinusoidal driving signal whose origin is the interaction of the two-level system with a quantum field. In this approach the driving field is replaced by a harmonic oscillator that is either strongly coupled to the TLS or populated with a large number of photons. Starting from the Rabi model, we derive expressions for the TLS's oscillation frequencies and compare the results with those obtained from the model where the driving signal is treated classically. We show that in the limits of weak coupling an…
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 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…
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…
Leveraging Landau-Zener-Stückelberg interference for accelerating diabatic quantum annealing
Qilimanjaro Quantum Tech.（Qilimanjaro量子技术）；Universitat de Barcelona（巴塞罗那大学）；Barcelona Supercomputing Center（巴塞罗那超级计算中心）；Sandia National Laboratories（桑迪亚国家实验室）
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 rate of electron-positron pair production in linearly polarized counter-propagating lasers is evaluated from a recently discovered solution of the time-dependent Dirac equation. The latter is solved in momentum space where it is formally equivalent to the Schrödinger equation describing a strongly driven two-level system. The solution is found from a simple transformation of the Dirac equation and is given in compact form in terms of the doubly-confluent Heun's function. By using the analogy with the two-level system, it is shown that for high-intensity lasers, pair production occurs throu…
We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time-independent if the transition probabilities alone are used. We add coherent control to the system, and increase the permitted maximum precision in this tim…
Quantum triangles can work as interferometers. Depending on their geometric size and interactions between paths, "beats" {\it and/or} "steps" patterns are observed. We show that when inter-level distances between level positions in quantum triangles periodically change with time, formation of beats {\it and/or} steps no longer depends only on the geometric size of the triangles but also on the characteristic frequency of the transverse signal. For large-size triangles, we observe the coexistence of beats {\it and} steps when the frequency of the signal matches that of non-adiabatic oscillation…
We present the first observation of Landau-Zener-Stückelberg (LZS) interference of the dressed states arising from an artificial atom, a superconducting phase qubit, interacting with a microwave field. The dependence of LZS interference fringes on various external parameters and the initial state of the qubit agrees quantitatively very well with the theoretical prediction. Such LZS interferometry between the dressed states enables us to control the quantum states of a tetrapartite solid-state system with ease, demonstrating the feasibility of implementing efficient multipartite quantum logic g…
We study the time evolution of a two-dimensional quantum particle exhibiting an energy spectrum, made of two bands, with two Dirac cones, as e.g. in the band structure of a honeycomb lattice. A force is applied such that the particle experiences two Landau-Zener transitions in succession. The adiabatic evolution between the two transitions leads to Stückelberg interferences, due to two possible trajectories in energy space. In addition to well-known dynamical and Stokes phases, the interference pattern reveals a geometric phase which depends on the chirality (winding number) and the mass sign …
Confinement-Tunable Synthetic Gauge Fields and Floquet Topological Phenomena in a Driven Quantum Wire Qubit
University of Abomey-Calavi（阿博梅-卡利维大学）；University of Dschang（德尚大学）；Quantum Materials and Computing Group - QMaCG（量子材料与计算群 - QMaCG）；Instituteur principal de l’enseignement général, Délégation Régionale de l’Ouest, Délégation Départementale de la Menoua, Arrondissement de Nkong-Ni, École Publique de Batsing’la Chefferie, Bafou, Cameroun（喀麦隆巴富，班辛拉酋长国公立学校，孔克尼区，梅努瓦省教育厅，西部大区教育厅，普通教育首席教师）；University of Yaoundé I（雅温得第一大学）
We theoretically demonstrate that nuclear spins can be harnessed to coherently control two-electron spin states in a double quantum dot. Hyperfine interactions lead to an avoided crossing between the spin singlet state and the ms = +1 triplet state, T_+ . We show that a coherent superposition of singlet and triplet states can be achieved using finite-time Landau-Zener-Stückelberg interferometry. In this system the coherent rotation rate is set by the Zeeman energy, resulting in ~1 nanosecond single spin rotations. We analyze the coherence of this spin qubit by considering the coupling to the n…
We study the Landau-Zener (LZ) dynamics in a setup of two Rydberg atoms with time-dependent detuning, both linear and periodic, using both the exact numerical calculations as well as the method of adiabatic impulse approximation (AIA). By varying the Rydberg-Rydberg interaction strengths, the system can emulate different three-level LZ models, for instance, bow-tie and triangular LZ models. The LZ dynamics exhibits non-trivial dependence on the initial state, the quench rate, and the interaction strengths. For large interaction strengths, the dynamics is well captured by AIA. In the end, we an…
Multipassage Landau-Zener tunneling oscillations in transverse/longitudinal dual dressing of atomic qubits
INO-CNR（意大利国家研究委员会光学研究所）；Dipartimento di Scienze Fisiche, della Terra e dell’Ambiente, Università degli Studi di Siena（锡耶纳大学地球与环境科学系）；Dipartimento di Fisica E. Fermi, Università of Pisa（比萨大学E.费米物理系）；NEST, Istituto Nanoscienze CNR（纳米科学研究所）；Technische Universität Berlin（柏林工业大学）；Department of Mathematical, Physical and Computer Sciences, University of Parma（帕尔马大学数学、物理与计算机科学系）；National Institute for Nuclear Physics (INFN), Milano Bicocca Section, Parma Group（意大利国家核物理研究所米兰比可卡分部帕尔马组）
Interfacing solid-state defect electron spins to other quantum systems is an ongoing challenge. The ground-state spin's weak coupling to its environment bestows excellent coherence properties, but also limits desired drive fields. The excited-state orbitals of these electrons, however, can exhibit stronger coupling to phononic and electric fields. Here, we demonstrate electrically driven coherent quantum interference in the optical transition of single, basally oriented divacancies in commercially available 4H silicon carbide. By applying microwave frequency electric fields, we coherently driv…
Time evolution of spin-orbit-coupled cold atoms in an optical lattice is studied, with a two-band energy spectrum having two avoided crossings. A force is applied such that the atoms experience two consecutive Landau-Zener tunnelings while transversing the avoided crossings. Stückelberg interference arises from the phase accumulated during the adiabatic evolution between the two tunnelings. This phase is gauge field-dependent and thus provides new opportunities to measure the synthetic gauge field, which is verified via calculation of spin transition probabilities after a double passage proces…
Electrons confined in Si quantum dots possess orbital, spin, and valley degrees of freedom (d.o.f.). We perform Landau-Zener-Stuckelberg-Majorana (LZSM) interferometry on a Si double quantum dot that is strongly coupled to a microwave cavity to probe the valley d.o.f. The resulting LZSM interference pattern is asymmetric as a function of level detuning and persists for drive periods that are much longer than typical charge decoherence times. By correlating the LZSM interference pattern with charge noise measurements, we show that valley-orbit hybridization provides some protection from the del…
The interaction of flux qubits with a low frequency tank circuit is studied. It is shown that changes in the state of the interacting qubits influence the effective impedance of the circuit, which is the essence of the so-called impedance measurement technique. The multiphoton resonant excitations in both single flux qubits and pairs of coupled flux qubits are investigated. In particular, we compare our theoretical results with recent spectroscopy measurements, Landau-Zener interferometry, and multiphoton fringes.
Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator's state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent results for the driven superconducting qubit-r…
