High-frequency suppression of inductive coupling between flux qubit and transmission line resonator

We perform theoretical calculations to investigate the naturally occurring high-frequency cutoff in a circuit comprising a flux qubit coupled inductively to a transmission line resonator (TLR). Our results agree with those of past studies that considered somewhat similar circuit designs. In particular, a decoupling occurs between the qubit and the high-frequency modes. As a result, the coupling strength between the qubit and resonator modes increases with mode frequency $\omega$ as $\sqrt{\omega}$ at low frequencies and decreases as $1/\sqrt{\omega}$ at high frequencies. We derive expressions for the multimode-resonator-induced Lamb shift in the qubit's characteristic frequency. Because of the natural decoupling between the qubit and high-frequency modes, the Lamb-shift-renormalized qubit frequency remains finite.Comment: 24 pages (preprint), 5 figure

Noise correlations in a flux qubit with tunable tunnel coupling

We have measured flux-noise correlations in a tunable superconducting flux qubit. The device consists of two loops that independently control the qubit's energy splitting and tunnel coupling. Low frequency flux noise in the loops causes fluctuations of the qubit frequency and leads to dephasing. Since the noises in the two loops couple to different terms of the qubit Hamiltonian, a measurement of the dephasing rate at different bias points provides a way to extract both the amplitude and the sign of the noise correlations. We find that the flux fluctuations in the two loops are anti-correlated, consistent with a model where the flux noise is generated by randomly oriented unpaired spins on the metal surface.Comment: 7 pages, including supplementary materia

Dynamical decoupling and dephasing in interacting two-level systems

We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our $1/f$ noise model. The results are applicable to any two-qubit system with transverse coupling, and they highlight the potential of decoupling techniques for improving two-qubit gate fidelities, an essential prerequisite for implementing fault-tolerant quantum computing

One photon simultaneously excites two atoms in a ultrastrongly coupled light-matter system

We experimentally investigate a superconducting circuit composed of two flux qubits ultrastrongly coupled to a common $LC$ resonator. Owing to the large anharmonicity of the flux qubits, the system can be correctly described by a generalized Dicke Hamiltonian containing spin-spin interaction terms. In the experimentally measured spectrum, an avoided level crossing provides evidence of the exotic interaction that allows the \textit{simultaneous} excitation of \textit{two} artificial atoms by absorbing \textit{one} photon from the resonator. This multi-atom ultrastrongly coupled system opens the door to studying nonlinear optics where the number of excitations is not conserved. This enables novel processes for quantum-information processing tasks on a chip.Comment: 11pages,5gigure

Nonclassicality of open circuit QED systems in the deep-strong coupling regime

We investigate theoretically how the ground state of a qubit-resonator system in the deep-strong coupling (DSC) regime is affected by the coupling to an environment. We employ as a variational ansatz for the ground state of the qubit-resonator-environment system a superposition of coherent states displaced in qubit-state-dependent directions. We show that the reduced density matrix of the qubit-resonator system strongly depends on how the system is coupled to the environment, i.e., capacitive or inductive, because of the broken rotational symmetry of the eigenstates of the DSC system in the resonator phase space. When the resonator couples to the qubit and the environment in different ways (for instance, one is inductive and the other is capacitive), the system is almost unaffected by the resonator-waveguide coupling. In contrast, when the two couplings are of the same type (for instance, both are inductive), by increasing the resonator-waveguide coupling strength, the average number of virtual photons increases and the quantum superposition realized in the qubit-resonator entangled ground state is partially degraded. Since the superposition becomes more fragile with increasing the qubit-resonator coupling, there exists an optimal coupling strength to maximize the nonclassicality of the qubit-resonator system.Comment: 24 pages, 11 figure

Single-photon-driven high-order sideband transitions in an ultrastrongly coupled circuit quantum electrodynamics system

We report the experimental observation of high-order sideband transitions at the single-photon level in a quantum circuit system of a flux qubit ultrastrongly coupled to a coplanar waveguide resonator. With the coupling strength reaching 10% of the resonator's fundamental frequency, we obtain clear signatures of higher-order red and first-order blue-sideband transitions, which are mainly due to the ultrastrong Rabi coupling. Our observation advances the understanding of ultrastrongly-coupled systems and paves the way to study high-order processes in the quantum Rabi model at the single-photon level.Comment: Accepted in Physical Review A. 12 pages, 6 figure

Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator

We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator ($\lambda/4$ CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency $\omega_{\rm{cutoff}}$ for the coupling between the FQ and the modes in the CPWR, where the coupling grows as $\sqrt{\omega_n}$ for $\omega_n/\omega_{\rm{cutoff}}\ll 1$ and decreases as $1/\sqrt{\omega_n}$ for $\omega_n/\omega_{\rm{cutoff}}\gg 1$. Here $\omega_n$ is the frequency of the $n$th mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above $\omega_{\rm{cutoff}}$ at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3\% and the total Lamb shift from all the modes is 96.5\%.Comment: 16 pages, 4 figure