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Journal of Surface Investigation X-ray Synchrotron and Neutron Techniques

Multiphoton resonances in a system of interacting josephson qubits

M. V. Denisenko, Сатанин Аркадий Михайлович

Published Nov 1, 2012• 0 citations
Publisher

Abstract

The behavior of the level population of two coupled qubits as a function of the system parameters and characteristics of the driving field has been studied. In the case where the tunneling splitting of qubit levels is small, the explicit expression for the transition probability describing multiphoton processes of any order and resonance conditions dependent on the qubit coupling constant have been obtained. The possibility of experimentally observing the discovered effects is discussed.

DOI
10.1134/s102745101212004x

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The behavior of the level population of two coupled qubits as a function of the system parameters and characteristics of the driving field has been studied. In the case where the tunneling splitting of qubit levels is small, the explicit expression for the transition probability describing multiphoton processes of any order and resonance conditions dependent on the qubit coupling constant have been obtained. The possibility of experimentally observing the discovered effects is discussed.
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.
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.
Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic \nscale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the \ndistance between the qubit energy levels and their populations and to read out the resonator's state, as well as the \nunavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum \nphenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent \nresults for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC \ncircuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a \nqubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. \nApplication of this theory allows to describe many phenomena for the single and two coupled superconducting \nqubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping \nand amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type \ncharacter, and creation of the inverse population for lasing.
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–resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing.
Resonant driving enables coherent control of quantum systems, including single and coupled qubits. From a complementary perspective, transitions of a quantum system can be exploited for the detection of microwave photons. In this work, we theoretically investigate resonant multiphoton excitations in a system of qubits. When the energy of K photons matches the energy splitting of the qubit system, the absorption of these photons leads to collective excitation of the qubits. We focus on the case of two coupled qubits and analyze the quantum dynamics of both excitation and relacation processes. In the particular case where only a single qubit is relevant and the remaining qubits can be neglected, the dynamics admits an analytical treatment. We examine multiphoton resonances, the Bloch-Siegert shift, and population inversion, phenomena that are central to both coherent quantum control and microwave photon detection.
Abstract We investigate a new type of multiphoton resonance in a four-level quantum system, where two of its levels are coupled strongly with two symmetric driving fields. Near the resonance condition where transitions occur, the different behaviors of the number of even and odd photons, n , is found to be consistent with experimental observations. By making all levels time-dependent, we compute the transition rates with resonant features. We explain this phenomenon in terms of groups of certain interfering trajectories of the multilevel systems, so that the behavior is insensitive to fluctuations of the energy of the driven levels, and survives deeply into the strong dephasing regime. Multiphoton resonances occur for the first time at the third order and for the second time at the fourth order of couplings and likewise for other higher orders. This study can be related to a variety of nanoscale solid state, atomic or molecular systems. An effective mechanism to explain previously implemented experiments in strongly driven double quantum dots is presented.