arXiv:1201.1901 · Physical Review B

Amplitude spectroscopy of two coupled qubits

Сатанин Аркадий Михайлович, M. V. Denisenko, Sahel Ashhab, Franco Nori

Published May 18, 2012• 43 citations

Abstract

We study the effect of a time-dependent driving field with a high amplitude on a system composed of two coupled qubits (two-level systems). Using the rotating-wave approximation (RWA) makes it possible to find simple conditions for resonant excitation of the four-level system. We find that the resonance conditions include the coupling strength between the qubits. Numerical simulations confirm the qualitative conclusions following from the RWA. To reveal the peculiarities of resonant transitions caused by the quasilevel motion and crossing in a periodic driving field, we use Floquet states, which determine the precise intermediate states of the system. Calculating the quasienergy states of the multilevel system makes it possible to find the transition probabilities and build interference patterns for the transition probabilities. The interference patterns demonstrate the possibility of obtaining various pieces of information about the qubits, since the positions of transition-probability maxima depend on various system parameters, including the coupling strength between the qubits.

DOI: 10.1103/physrevb.85.184524

Related papers

Quasi-energies of coupled qubits: Magnus-Floquet states and their probing by weak signal

M. V. Bastrakova, N. V. Klenov, Сатанин Аркадий Михайлович

The behaviour of two coupled qubits in a periodic electromagnetic field of arbitrary amplitude was investigated. Quasienergy levels of the system as a function of the driving field parameters and the qubit coupling energy were found on the basis of the Floquet theory and the Magnus approximation. It is shown that the quasienergy levels may intersect depending on the control parameters. This fact can manifest itself as appearance of the novel resonances and interesting nonlinear phenomena.

Journal of Physics Conference SeriesFeb 1, 20190 citations

Dissipative dynamics of a qubit-oscillator system in the ultrastrong coupling and driving regimes

Johannes Hausinger

The model of a two-level system (TLS) coupled to a harmonic oscillator has found a widespread application in physics and chemistry. In this thesis we focus on the field of circuit quantum electrodynamics where the TLS stands for a quantum bit (qubit), which is the basic building unit of a potential quantum computer, and the oscillator represents a transmission-line resonator, which can be used, e.g., to store information contained on the qubit or for communication between several qubits. Furthermore, the oscillator can model a superconducting quantum interference device (SQUID) determining the state of the qubit. In first experimental realizations the coupling between the qubit and the oscillator was small compared to characteristic frequencies of the two devices. In such a situation the Jaynes-Cummings model provides a realistic and completely analytical description of the energy spectrum and the dynamics of the setup. However, it relies on a rotating-wave approximation (RWA) which neglects counter-rotating terms in the full qubit-oscillator Hamiltonian. These counter-rotating terms become important under increase of the coupling strength, as it has been achieved in recent experiments. We present two analytical approaches to take these additional contributions into account: The first one treats the qubit-oscillator Hamiltonian perturbatively in the coupling strength and predicts a frequency shift in its energy spectrum, the Bloch-Siegert shift. The second one considers the qubit's tunneling splitting as small parameter and thus treats the problem to all orders in the coupling allowing to enter the ultrastrong coupling regime, where the coupling strength becomes comparable to the qubit's and/or oscillator's frequency. For both cases we give a thorough analysis of the qubit's dynamics. In order to perform operations the qubit is usually probed by an external driving force. We model this situation by coupling the TLS to a classical oscillator and examine the resulting time dependent Hamiltonian using a combination of Floquet theory and Van Vleck perturbation theory. Thus, we provide an analysis of the qubit's energy spectrum and dynamics which is nonperturbative in the driving amplitude. We investigate effects like coherent destruction of tunneling and driving-inducing tunneling oscillations. By coupling the driven TLS to a quantized oscillator we give for the first time an analytical treatment of the qubit-oscillator system being simultaneously exposed to both ultrastrong coupling and extreme driving. We observe interesting phenomena in the dynamics like the suppression of specific frequencies under a variation of the coupling strength. To mimic environmental influences on the qubit we apply the Caldeira-Leggett master equation approach to the driven TLS and to the qubit-oscillator system and provide for both cases analytical expressions for the relaxation and dephasing rates.

Jan 1, 20100 citations

Dynamics of a two-level system under strong driving: Quantum-gate optimization based on Floquet theory

Chunqing Deng, Feiruo Shen, Sahel Ashhab +1 more

We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is nonadiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet interference efficient suppression of transitions in the adiabatic basis (FIESTA), that can be used to design ultrafast high-fidelity single-qubit quantum gates.

arXiv:1605.08826Physical Review ASep 27, 201645 citations

Large-amplitude harmonic driving of highly coherent flux qubits

Alejandro Ferrón, Daniel Domı́nguez, María José Sánchez

The device for the Josephson flux qubit can be considered as a solid-state artificial atom with multiple energy levels. When a large-amplitude harmonic excitation is applied to the system, transitions at the energy levels avoided crossings produce visible changes in the qubit population over many driven periods that are accompanied by a rich pattern of interference phenomena. We present a Floquet treatment of the periodically time-dependent Schr\"odinger equation of the strongly driven qubit beyond the standard two-level approach. For low amplitudes, the average probability of a given sign of the persistent current qubit exhibits, as a function of the static flux detuning and the driving amplitude, Landau-Zener-St\"uckelberg (LZS) interference patterns that evolve into complex diamondlike patterns for large amplitudes. In the case of highly coherent flux qubits we show that the higher-order diamonds can not be simply described relying on LZS transitions in each avoided crossing considered separately. In addition we propose a spectroscopic method based on starting the system in the first excited state instead of in the ground state, which can give further information on the energy-level spectrum and dynamics in the case of highly coherent flux qubits. We compare our numerical results with recent experiments that perform amplitude spectroscopy to probe the energy spectrum of the artificial atom.

arXiv:1006.3505Physical Review BOct 19, 201020 citations

Control of spectroscopic features of multiphoton transitions in two coupled qubits by driving fields

V. O. Munyaev, M. V. Bastrakova

The quantum level population behavior of two coupled flux qubits depending on the external driving field characteristics is studied. Explicit expressions for the multiphoton transition probabilities at an arbitrary control field amplitude are obtained for the case of small tunnel splitting energies. We describe the controllable features of their formation and thereby the creation or destruction of entanglement on the direct interlevel transition and during the transition through intermediate states by system bias tuning. We found a feature of the qubit population inversion that results in the independence of the resonance positions from the qubit coupling strength. Using the Floquet-Markov equation, we numerically demonstrate that the positions of multiphoton resonances are stable to dissipative processes.

arXiv:2103.14285Physical Review AJul 26, 20219 citations

Tunable quantum interfaces between superconducting qubits and microwave photons induced by extreme driving

Byoung-moo Ann

In this work, I investigate how to implement and quantify \\emph{in-situ} tunable quantum interface between superconducting qubits and resonators using external transverse driving fields beyond the rotating wave approximation (RWA). When studying the system under the time-periodic driving field, we typically rely on RWA, a useful technique that significantly reduces the analytical difficulties in solving the dynamics with time-dependent Hamiltonian. Nonetheless, it does not correctly describe the systems' dynamics when the drive fields are excessively strong and far off-resonant. Especially in circuit QED platform, the RWA often breakdowns. Many studies before, however, mainly focus on the transition frequency shifts. How the RWA distorts the interaction rates between two systems has been rarely explored. I have performed quantitative studies over two different systems. One is the quantum Rabi model (QRM) where a two-level atom is dispersively coupled to a resonator mode. The other is dispersively coupled a transmon and resonator system, which is the same as the QRM except that the transmon replaces the two-level atom in QRM. In both cases, I have revealed that the RWA significantly mislead the sideband transition rates between two elements. In the latter case, I have performed the experiments, and the results nicely agree with the analytical and numerical calculations. In addition to these, I also have introduced a study where the tunable coupling between a transmon and resonator is used for non-invasive resonator probing.

Jul 2, 20210 citations