Dephasing of a Superconducting Qubit Induced by Photon Noise

Abstract

We have studied the dephasing of a superconducting flux qubit coupled to a dc-SQUID based oscillator. By varying the bias conditions of both circuits we were able to tune their effective coupling strength. This allowed us to measure the effect of such a controllable and well-characterized environment on the qubit coherence. We can quantitatively account for our data with a simple model in which thermal fluctuations of the photon number in the oscillator are the limiting factor. In particular, we observe a strong reduction of the dephasing rate whenever the coupling is tuned to zero. At the optimal point we find a large spinecho decay time of 4 s. DOI: 10.1103/PhysRevLett.95.257002 PACS numbers: 74.50.+r, 03.67.Lx, 73.40.Gk Retaining quantum coherence is a central requirement in quantum information processing. Solid-state qubits, including superconducting ones [1][2][3], couple to environmental degrees of freedom that potentially lead to dephasing. This dephasing is commonly associated with lowfrequency noise [4]. However, resonant modes at higher frequencies are harmful as well. In resonance with the qubit transition they favor energy relaxation. Off resonance they may cause pure dephasing, due to fluctuations of the photon number stored in the oscillator. Experimentally we show that the quantum coherence of our superconducting flux qubit coupled to a dc-SQUID oscillator is limited by the oscillator thermal photon noise. By tuning the qubit and SQUID bias conditions we can suppress the influence of photon noise, and we measure a strong enhancement of the spin-echo decay time from about 100 ns to 4 s.In our experiment, a flux qubit of energy splitting h q is coupled to a harmonic oscillator of frequency p which consists of a dc SQUID and a shunt capacitor [5,6]. The oscillator is weakly damped with a rate and is detuned from the qubit frequency. In this dispersive regime, the presence of n photons in the oscillator induces a qubit frequency shift following q;n ÿ q;0 n 0 , where the shift per photon 0 depends on the effective oscillatorqubit coupling. Any fluctuation in n thus causes dephasing. Taking the oscillator to be thermally excited at a temperature T and assuming the pure dephasing time 1=, we find [7], after a reasoning similar to [8], n n 12 0 2with the average photon number stored in the oscillator n exph p =kT ÿ 1 ÿ1 . We note that a similar effect was observed in a recent experiment on a charge qubit coupled to a slightly detuned waveguide resonator [9]. When driving the oscillator to perform the readout, the authors observed a shift and a broadening of the qubit resonance due to the ac-Stark shift and to photon shot noise, well-known in atomic cavity quantum electrodynamics [10]. In our experiments, the oscillator is not driven but thermally excited. In addition, we are able to tune in situ the coupling constant and 0 and, therefore, to directly monitor the decohering effect of the circuit.Our flux qubit consists of a micron-size superconducting aluminum loop intersected by four Josephson junctio...

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