Amplitude spectroscopy of two coupled qubits

Abstract

We study the effect of a time-dependent driving field with a large 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 quasi-level motion and crossing in a periodic driving field, we use Floquet states, which determine the precise intermediate states of the system. Calculating the quasi-energy states of the multi-level 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.

Probe spectroscopy of quasienergy states

“…The τ -periodic part of the weak probe becomes simplyF S =σ z , operating between the resonant basis states of the RWA Hamiltonian (17). In the diagonalization of the strongly driven part of the Hamiltonian, the perturbation matrix gets a non-diagonal form…”

“…Thus, the transition amplitude depends only on the coupling strength ∆J n (A/ ω) of the two uncoupled energy levels in Eq. (17). The comparison between the numerical (solid) and analytical (dotted) transition amplitudes is shown in Fig.…”

“…The formalism is enjoying a revival due to the generation of novel systems allowing strong driving fields and long enough coherence times, e.g. superconducting qubits and circuits 6,[14][15][16][17][18][19][20][21] , and topological insulators 22 . The Floquet formalism [23][24][25] is a semiclassical method that can be understood as a limiting case of a full quantum mechanical picture when the number of quanta in the driving field is large 23 .…”

Multiphoton transitions in Josephson-junction qubits (Review Article)

“…Being excited by a resonant microwave field, they display one-photon transitions [44][45][46][47][48][49][50][51]. Alternatively, at smaller frequencies, the two-qubit systems can experience multiphoton transitions [52][53][54][55].…”

Delayed-response quantum back action in nanoelectromechanical systems

“…(i) This can be created by means of non-adiabatic Landau-Zener transitions between the energy levels [46][47][48][49][50]. (ii) The 50/50-beam-splitting can be created by resonantly driving the TLS as in Ref.…”