Nonlinear spectroscopy of superconducting anharmonic resonators

Abstract

We formulate a model for the steady state response of a nonlinear quantum oscillator structure, such as those used in a variety of superconducting qubit experiments, when excited by a steady, but not necessarily small, ac tone. We show that this model can be derived directly from a circuit description of some recent qubit experiments in which the state of the qubit is read out directly, without a SQUID magnetometer. The excitation profile has a rich structure depending on the detuning of the tone from the small-signal resonant frequency, on the degree of damping, and on the excitation amplitude. We explore two regions in detail: First, at high damping there is a trough in the excitation response as a function of detuning, near where the classical Duffing bifurcation occurs. This trough has been understood as a classical interference between two metastable responses with opposite phase. We use Wigner function studies to show that while this picture is roughly correct, there are also more quantum mechanical aspects to this feature. Second, at low damping we study the emergence of sharp, discrete spectral features from a continuum response. We show that these the structures, associated with discrete transitions between different excited-state eigenstates of the oscillator, provide an interesting example of a quantum Fano resonance. The trough in the Fano response evolves continuously from the "classical" trough at high damping.

Photon blockade and the quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator

“…This is the Hamiltonian operator of the quantum Duffing model. The Duffing model has received a considerable attention in the recent literature [51][52][53][54][55][56] especially in the context of superconducting transmon realizations. It is worthwhile to notice that in this regime the potential is no longer periodic and, thus, we can neglect the periodic boundary condition of the wavefunction.…”

Nonlinearity-induced entanglement stability in a qubit-oscillator system

“…In fact, quantum nonlinear oscillators (NLO) have been implemented in several settings, including trapped ions (where the trapping potential can be modified to include nonlinearities [19]), optomechanical systems (where tunable nonlinearities have been realized [20]), and atoms in optical lattices [21]. Interestingly, it has been shown that the inclusion of strong enough nonlinearities in the oscillator potential allows new possibilities to generate non-classical states [22][23][24][25][26][27]. However, despite the promising experimental progresses in the control and fabrication of NLO, it is still a challenge to achieve significant nonlinearities (for a more detailed * Electronic address: v.montenegro.11@ucl.ac.uk † Electronic address: a.ferraro@qub.ac.uk ‡ Electronic address: sougato@theory.phys.ucl.ac.uk discussion about the nonlinear regimes and their possible experimental implementations see Sec.…”

Protecting two-qubit quantum states byπ-phase pulses

“…Such quantum decoherence can often cause severe distortion to a quantum state rendering many quantum systems in the real world useless [3][4][5][6][7][8][9][10]. In order to protect a quantum state, many methods against decoherence have been studied.…”

“…The interaction between a quantum system and its environment inevitably leads to the decoherence [1,2] of a quantum state. Such quantum decoherence can often cause severe distortion to a quantum state rendering many quantum systems in the real world useless [3][4][5][6][7][8][9][10]. In order to protect a quantum state, many methods against decoherence have been studied.…”