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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum decoherence of a single ion qubit induced by photon-number fluctuations

Moonjoo Lee, Konstantin Friebe, Florian R. Ong, Dario Fioretto, Klemens Schüppert, R. Blatt, Tracy E. Northup

Published Sep 13, 2016• 0 citations

Abstract

Quantum measurement is based on the interaction between a quantum object and a meter entangled with the object. While information about the object is being extracted by the interaction, the quantum fluctuations of the object are imprinted onto the meter as a form of decoherence. Here, we study the nondestructive reconstruction of the photon number in an optical cavity, harnessing the quantum decoherence. We consider a single 40Ca+ ion that is dispersively coupled to a high-finesse cavity. While the cavity is populated with weak coherent states, Ramsey spectroscopy is performed on the qubit transition to identify the shift and the broadening of the atomic energy levels. The shift is due to the ac Stark effect induced by cavity photons, and the broadening is attributed to the photon-number fluctuations of the cavity field. We show theoretically that photon-number distributions of the intracavity fields can be reconstructed in a basis of up to eleven Fock states with the maximum likelihood method. Furthermore, we show that the photon number of each polarization component can also be reconstructed, taking advantage of the rich energy-level structure of the ion. In combination with currently available mirror-coating technology, quantum non-demolition (QND) measurement of cavity photons will make it possible to create and manipulate nonclassical cavity-field states in the optical domain.

DOI: 10.1117/12.2238503

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We dispersively couple a single trapped ion to an optical cavity to extract information about the cavity photon-number distribution in a nondestructive way. The photon-number-dependent ac Stark shift experienced by the ion is measured via Ramsey spectroscopy. We use these measurements first to obtain the ion-cavity interaction strength. Next, we reconstruct the cavity photon-number distribution for coherent states and for a state with mixed thermal-coherent statistics, finding overlaps above 99% with the calibrated states.

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We have performed spectroscopy of a superconducting charge qubit coupled nonresonantly to a single mode of an on-chip resonator. The strong coupling induces a large ac Stark shift in the energy levels of both the qubit and the resonator. The dispersive shift of the resonator frequency is used to nondestructively determine the qubit state. Photon shot noise in the measurement field induces qubit level fluctuations leading to dephasing which is characteristic for the measurement backaction. A crossover in line shape with measurement power is observed and theoretically explained. For weak measurement a long intrinsic dephasing time of T2>200 ns of the qubit is found.

When atoms are illuminated by an off-resonant field, the AC Stark effect will lead to phase shifts in atomic states. The phase shifts are proportional to the photon number of the off-resonant illuminating field. By measuring the atomic phase with newly developed atom-light hybrid interferometers, we can achieve quantum non-demolition measurement of the photon number of the optical field. In this paper, we analyze theoretically the performance of this QND measurement scheme by using the QND measurement criteria established by Holland et al [Phys. Rev. A 42, 2995 (1990)]. We find the quality of the QND measurement depends on the phase resolution of the atom-light hybrid interferometers. We apply this QND measurement scheme to a twin-photon state from parametric amplifier to verify the photon correlation in the twin beams. Furthermore, a sequential QND measurement procedure is analyzed for verifying the projection property of quantum measurement and for the quantum information tapping. Finally, we discuss the possibility for single-photon-number-resolving detection via QND measurement.

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We theoretically study measurement-induced dephasing of a superconducting qubit in the circuit QED architecture and compare the results to those obtained experimentally by Schuster et al. [Phys. Rev. Lett. 94, 123602 (2005)]. Strong coupling of the qubit to the resonator leads to a significant ac Stark shift of the qubit transition frequency. As a result, quantum fluctuations in the photon number populating the resonator cause dephasing of the qubit. We find good agreement between the predicted line shape of the qubit spectrum and the experimental results. Furthermore, in the strongly dispersive limit, where the Stark shift per photon is large compared to the cavity decay rate and the qubit linewidth, we predict that the qubit spectrum will be split into multiple peaks, with each peak corresponding to a different number of photons in the cavity.