Strong Coupling of a Quantum Oscillator to a Flux Qubit at Its Symmetry Point

Abstract

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 of which the gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We show full spectroscopy of the qubit-oscillator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency νosc we find the largest vacuum Rabi splitting of ∼ 0.1νosc. Here being at resonance coincides with the optimal coherence of the symmetry point.Superconducting qubits coupled to quantum oscillators have demonstrated a remarkable richness of physical phenomena in the last few years. After the first reports of coherent state transfer and strong coupling [1, 2], we have witnessed a rapid development of the field called circuit quantum electrodynamics (CQED) using high quality superconducting oscillators in realizing quantum gates [3], algorithms [4] as well as non-classical states of light and matter in artificially fabricated structures [5,6]. Among the different implementations the transmon [1,[3][4][5] and the phase qubit [6] dominated this development. With flux qubits the avoided crossing between qubit and oscillator level was observed [7,8] and the coherent single-photon exchange between qubit and oscillator was demonstrated [8]. However the, coherence of the flux qubit is optimally preserved only in the symmetry point for flux bias, where the energy splitting is minimal. This minimal splitting (h∆) is called the gap and depends (exponentially) on the properties of the Josephson junctions. Therefore, the gap is hard to control in fabrication and it is impossible to make it coincide with a fixed oscillator frequency. We now have developed a flux qubit of which the gap ∆ can be tuned over a broad range on sub-ns time scales [9]. With the use of this control we demonstrate strong coupling of a flux qubit with good coherence to a lumped-element LC oscillator, showing fast and longlived vacuum Rabi oscillations.Parameters of the superconducting qubits can be to a large extent chosen in the design phase. For strong coupling, where the interaction strength g exceeds the cavity and qubit loss rates, the rotating-wave approximation (RWA) can be applied and the system can be described by a Jaynes-Cummings type Hamiltonian. If g approaches the qubit or oscillator frequencies the RWA no longer holds, leading into the ultra-strong coupling regime [10,11]. For a flux qubit the ratio g/ν osc can be an order of magnitude larger than for charge and phase qubits [12], while these latter devices have a coupling that can be several orders of magnitude larger than the atomlight interaction energy [1]. For good coherence, operating the qubit at its spectral symmetry point is required. Therefore, experimentally combining galvanic coupling of oscillator and flux qubit with this symmetry point operation provides a major step forward in the development of CQED systems. For the flux qubit at the symmetry point the anharmonicity (distance ...

Microwave quantum optics and electron transport through a metallic dot strongly coupled to a transmission line cavity

“…In this regime the JaynesCummings model breaks down and new physical effects become important. Recent experiments [21][22][23] with flux qubits directly coupled to a superconductor transmission line cavity demonstrated couplings of the order of ten percent of the resonator frequency. These findings spurred a number of theoretical works on microwave quantum optics in the ultrastrong regime, see e.g.…”

Light-shift-induced quantum phase transitions of a Bose-Einstein condensate in an optical cavity

“…In the case of the RWA, its energy spectrum and wavefunctions can be solved exactly [2]. With the rapid development of fabricated technique in solid-state systems, the Jaynes-Cummings model can be realized in semiconducting dots [3][4][5][6] and superconducting Josephson junctions [7][8][9][10][11][12]. More importantly, recent experiment has reported the existence of the ultrastrong coupling with the ratio 0.12 between the coupling strength and the microwave photon frequency [13].…”

Driven Dynamics and Rotary Echo of a Qubit Tunably Coupled to a Harmonic Oscillator

“…In this work, we study an additional consequence of the resonator by investigating the driven dynamics and the dephasing of a flux qubit [16] that is tunably coupled to a harmonic oscillator [17][18][19][20]. We find that the resonator mediates an indirect driving field that interferes with the direct drive set by the qubit-antenna coupling, thereby modifying both the amplitude and the phase of the net driving field.…”

“…Microwave resonators also provide a means to couple distant qubits [11,12] and, in this role, have been used to implement quantum algorithms in superconducting circuits [13] and to develop quantum computer architectures [14]. However, the coupling of a qubit to a resonator also influences the qubit coherence, for example by modifying its relaxation rate through the Purcell effect [15].In this work, we study an additional consequence of the resonator by investigating the driven dynamics and the dephasing of a flux qubit [16] that is tunably coupled to a harmonic oscillator [17][18][19][20]. We find that the resonator mediates an indirect driving field that interferes with the direct drive set by the qubit-antenna coupling, thereby modifying both the amplitude and the phase of the net driving field.…”