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Register a new userLadder of Loschmidt anomalies in the deep strong-coupling regime of a qubit-oscillator system
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We uncover a remarkably regular array of singularity-like structures within the deep strong-coupling limit of qubit-oscillator (e.g. light-matter) systems described by the quantum Rabi model, as a function of time and coupling strength. These non-analytic anomalies in the Loschmidt amplitude (echoes) suggest the existence of new forms of dynamical phase transition within this deep strong-coupling regime. The key feature whereby the initial state collapses into orthogonal states at select values of the interaction strength and select times, may be used to enhance - or attack - quantum information processing or computation schemes that rely on removing - or retaining - a given quantum state.
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The Jaynes-Cummings model, describing the interaction between a single two-level system and a photonic mode, has been used to describe a large variety of systems, ranging from cavity quantum electrodynamics, trapped ions, to superconducting qubits coupled to resonators. Recently there has been renewed interest in studying the quantum strong-coupling (QSC) regime, where states with photon number greater than one are excited. This regime has been recently achieved in semiconductor nanostructures, where a quantum dot is trapped in a planar microcavity. Here we study the quantum strong-coupling regime by calculating its photoluminescence (PL) properties under a pulsed excitation. We discuss the changes in the PL as the QSC regime is reached, which transitions between a peak around the cavity resonance to a doublet. We particularly examine the variations of the PL in the time domain, under regimes of short and long pulse times relative to the microcavity decay time.
We measure the dispersive energy-level shift of an $LC$ resonator magnetically coupled to a superconducting qubit, which clearly shows that our system operates in the ultrastrong coupling regime. The large mutual kinetic inductance provides a coupling energy of $approx0.82$~GHz, requiring the addition of counter-rotating-wave terms in the description of the Jaynes-Cummings model. We find a 50~MHz Bloch-Siegert shift when the qubit is in its symmetry point, fully consistent with our analytical model.
We report on experimentally measured light shifts of superconducting flux qubits deep-strongly coupled to LC oscillators, where the coupling constants are comparable to the qubit and oscillator resonance frequencies. By using two-tone spectroscopy, the energies of the six lowest levels of each circuit are determined. We find huge Lamb shifts that exceed 90% of the bare qubit frequencies and
We derive the Hamiltonian of a superconducting circuit that comprises a single-Josephson-junction flux qubit and an LC oscillator. If we keep the qubits lowest two energy levels, the derived circuit Hamiltonian takes the form of the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator, regardless of the coupling strength. To investigate contributions from the qubits higher energy levels, we numerically calculate the transition frequencies of the circuit Hamiltonian. We find that the qubits higher energy levels mainly cause an overall shift of the entire spectrum, but the energy level structure up to the seventh excited states can still be fitted well by the quantum Rabi Hamiltonian even in the case where the coupling strength is larger than the frequencies of the qubit and the oscillator, i.e., when the qubit-oscillator circuit is in the deep-strong-coupling regime. We also confirm that some of the paradoxical properties of the quantum Rabi Hamiltonian in the deep-strong-coupling regime, e.g. the non-negligible number of photons and the nonzero expectation value of the flux in the oscillator in the ground state, arise from the circuit Hamiltonian as well.
A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit whose gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We show full spectroscopy of the qubit-resonator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency $ u_{osc}$ we find the strongest qubit-resonator coupling ($g/hsim0.1 u_{rm osc}$). Here being at resonance coincides with the optimal coherence of the symmetry point. Significant further increase of the coupling is possible.
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