Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime

Forn-Díaz, P.; Lisenfeld, Jürgen; Marcos, D. Crespo; García-Ripoll, Juan José; Solano, E.; Harmans, C.J.P.M.; Mooij, J. E.

doi:10.1103/physrevlett.105.237001

Cited by 719 publications

(911 citation statements)

References 26 publications

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“…Also, when the qubit drive is tuned close to the resonator frequency oEo r and when the driving amplitude g is large and equal to the frequency of the modulation g ¼ O, the system can be seen as a realization of a quantum simulator of the ultrastrong coupling regime 22,23 . In our set-up, the simulated coupling rate is estimated to reach over 10% of the effective resonator frequency (see Supplementary Note S3), comparable to earlier reports 24,25 where the ultrastrong coupling was obtained by sample design. The sinusoidal modulation allows a different perspective on motional averaging.…”

Section: Resultssupporting

confidence: 87%

Motional averaging in a superconducting qubit

et al. 2013

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Superconducting circuits with Josephson junctions are promising candidates for developing future quantum technologies. Of particular interest is to use these circuits to study effects that typically occur in complex condensed-matter systems. Here we employ a superconducting quantum bit-a transmon-to perform an analogue simulation of motional averaging, a phenomenon initially observed in nuclear magnetic resonance spectroscopy. By modulating the flux bias of a transmon with controllable pseudo-random telegraph noise we create a stochastic jump of its energy level separation between two discrete values. When the jumping is faster than a dynamical threshold set by the frequency displacement of the levels, the initially separate spectral lines merge into a single, narrow, motional-averaged line. With sinusoidal modulation a complex pattern of additional sidebands is observed. We show that the modulated system remains quantum coherent, with modified transition frequencies, Rabi couplings, and dephasing rates. These results represent the first steps towards more advanced quantum simulations using artificial atoms.

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Section: Resultssupporting

confidence: 87%

Motional averaging in a superconducting qubit

et al. 2013

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“…3c). In contrast, the highest coupling strengths achieved in previous experiments 12,13 give g /ω o = 0.12 and 0.1, respectively. From the spectrum in Fig.…”

Section: Nature Physicsmentioning

confidence: 58%

Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime

et al. 2016

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The interaction between an atom and the electromagnetic field inside a cavity 1-6 has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies, including lasers and many quantum computing architectures. Superconducting qubits 7,8 have allowed the realization of strong 9,10 and ultrastrong 11-13 coupling between artificial atoms and cavities. If the coupling strength g becomes as large as the atomic and cavity frequencies (∆ and ω o , respectively), the energy eigenstates including the ground state are predicted to be highly entangled 14 . There has been an ongoing debate 15-17 over whether it is fundamentally possible to realize this regime in realistic physical systems. By inductively coupling a flux qubit and an LC oscillator via Josephson junctions, we have realized circuits with g/ω o ranging from 0.72 to 1.34 and g/∆ 1. Using spectroscopy measurements, we have observed unconventional transition spectra that are characteristic of this new regime. Our results provide a basis for ground-state-based entangled pair generation and open a new direction of research on strongly correlated light-matter states in circuit quantum electrodynamics.We begin by describing the Hamiltonian of each component in the qubit-oscillator circuit, which comprises a superconducting flux qubit and an LC oscillator inductively coupled to each other by sharing a tunable inductance L c , as shown in the circuit diagram in Fig. 1a.The Hamiltonian of the flux qubit can be written in the basis of two states with persistent currents flowing in opposite directions around the qubit loop 18 , |L q and |R q , as H q = − (∆σ x + εσ z )/2, where ∆ and ε = 2I p 0 (n φq − n φq0 ) are the tunnel splitting and the energy bias between |L q and |R q , I p is the maximum persistent current, and σ x, z are Pauli matrices. Here, n φq is the normalized flux bias through the qubit loop in units of the superconducting flux quantum, 0 = h/2e, and n φq0 = 0.5 + k q , where k q is the integer that minimizes |n φq − n φq0 |. The macroscopic nature of the persistent-current states enables strong coupling to other circuit elements. Another important feature of the flux qubit is its strong anharmonicity: the two lowest energy levels are well isolated from the higher levels.The Hamiltonian of the LC oscillator can be written asC is the resonance frequency, L 0 is the inductance of the superconducting lead, L qc ( L c ) is the inductance across the qubit and coupler (see Supplementary Section 2), C is the capacitance, andâ (â † ) is the oscillator's annihilation (creation) operator. Figure 1b shows a laser microscope image of the lumped-element LC oscillator, where L 0 is designed to be as small as possible to maximize the zeropoint fluctuations in the currentand hence achieve strong coupling to the flux qubit, while C is adjusted so as to achieve a desired value of ω o . The freedom of choosing L 0 for large I zpf is one of the advantages of lumped-element LC oscillators over coplanar-waveguide ...

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“…Pioneered by the experiments of Refs. [12,13], experiments in the DSC regime have now been achieved with flux qubits coupled to resonators [14] as well as an electromagnetic continuum [15]. Additionally, the U/DSC coupling regime of the Rabi model was the subject of recent analog quantum simulations [16,17].…”

Section: Introductionmentioning

confidence: 99%

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

et al. 2017

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In this experiment, we couple a superconducting transmon qubit to a high-impedance 645 microwave resonator. Doing so leads to a large qubit-resonator coupling rate g, measured through a large vacuum Rabi splitting of 2g 910 MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies ω, placing our system close to the ultrastrong coupling regime (ḡ = g/ω = 0.071 on resonance). Combining this setup with a vacuum-gap transmon architecture shows the potential of reaching deep into the ultrastrong couplingḡ ∼ 0.45 with transmon qubits.

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Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime

Cited by 719 publications

References 26 publications

Motional averaging in a superconducting qubit

Motional averaging in a superconducting qubit

Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime

Approaching ultrastrong coupling in transmon circuit QED using a high-impedance resonator

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