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arXiv:1206.0360 · Physical Review A

Theory of Josephson photomultipliers: Optimal working conditions and back action

Luke C. G. Govia, Emily Pritchett, Seth Merkel, Deanna Pineau, Frank K. Wilhelm

Published Sep 11, 2012• 34 citations
arXivHTMLPDF

Abstract

We describe the back action of microwave-photon detection via a Josephson photomultiplier (JPM), a superconducting qubit coupled strongly to a high-quality microwave cavity. The back-action operator depends qualitatively on the duration of the measurement interval, resembling the regular photon annihilation operator at short interaction times and approaching a variant of the photon subtraction operator at long times. The optimal operating conditions of the JPM differ from those considered optimal for processing and storing of quantum information, in that a short ${T}_{2}$ of the JPM suppresses the cavity dephasing incurred during measurement. Understanding this back action opens the possibility of performing multiple JPM measurements on the same state, hence performing efficient state tomography.

DOI
10.1103/physreva.86.032311

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We describe the back action of microwave-photon detection via a Josephson photomultiplier (JPM), a superconducting qubit coupled strongly to a high-quality microwave cavity. The back-action operator depends qualitatively on the duration of the measurement interval, resembling the regular photon annihilation operator at short interaction times and approaching a variant of the photon subtraction operator at long times. The optimal operating conditions of the JPM differ from those considered optimal for processing and storing of quantum information, in that a short T2{T}_{2}T2​ of the JPM suppresses the cavity dephasing incurred during measurement. Understanding this back action opens the possibility of performing multiple JPM measurements on the same state, hence performing efficient state tomography.
This thesis describes the back action of microwave-photon detection via a Josephson photomultiplier (JPM), a superconducting qubit coupled strongly to a high-quality mi- crowave cavity, and the applications of these devices. The back action operator depends qualitatively on the duration of the measurement interval, resembling the regular photon annihilation operator at short interaction times and approaching a variant of the photon subtraction operator at long times. The optimal operating conditions of the JPM differ from those considered optimal for processing and storing of quantum information, in that a short T2 of the JPM suppresses the cavity dephasing incurred during measurement. Un- derstanding this back action opens the possibility to perform multiple JPM measurements on the same state, hence performing efficient state tomography. In addition, this the- sis describes the creation of non-classical states of microwave radiation via single photon detection using JPMs. When operated in the low T2 regime, the back action of a JPM resembles the photon subtraction operator. Using the non-linearity of this back action, it is possible to create non-classical states of microwave radiation, including squeezed vacuum and odd Schro ̈dinger cat states, starting from a coherent state.
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We propose a viable design of a microwave two-photon threshold detector. In essence, the considered scheme is an extension of the existing single-photon detector—a Josephson photomultiplier (JPM)—an absorbing microwave detector based on a capacitively shunted rf superconducting quantum interference device (SQUID). To implement a two-photon threshold detector, we utilize a dimer of resonators—two lumped-element resonators interacting via an asymmetric dc SQUID, with one of the resonators capacitively coupled to the JPM. By specific tuning of the resonator frequencies and the external flux through the dc SQUID coupler, we engineer a nonperturbative two-photon coupling between the resonators. This coupling results in the coherent conversion of a photon pair from one resonator into a single photon in another resonator, enabling selective response to quantum states with at least two photons. We also consider an extended coupler design that allows on-demand switching of two-photon coupling. In addition, we propose the modified JPM design to improve its performance. Our calculations demonstrate that, for realistic circuit parameters, we can achieve more than 99 % fidelity of photon pair detection in less than 50 ns. The considered scheme may serve as a building block for the implementation of efficient photon-number-resolving detectors in circuit QED architecture.
We study counting photons confined in a mode of a microwave resonator via repeated measurements by a Josephson photomultiplier (JPM). The considered JPM is essentially a flux-biased phase qubit operating as a single-photon detector. We identify optimal operational regimes that maximize photon-number resolution within a predetermined range. Two counting techniques are studied. The first is to count the total number of clicks in the measurement sequence. The second involves counting the number of clicks until the occurrence of either the first no-click event or the end of the measurement sequence. Our theoretical methods employ the derived positive operator-valued measures for the considered photocounting techniques and the introduced measure of the photon-number resolution. The results reveal that the resolution decrease in both cases is mainly caused by the JPM relaxation. As an example, we show how the obtained results can be used for practical testing nonclassical properties of electromagnetic radiation in a microwave resonator.
We describe an approach to the high-fidelity measurement of a superconducting qubit using an on-chip microwave photon counter.The protocol relies on the transient response of a dispersively coupled measurement resonator to map the state of the qubit to "bright" and "dark" cavity pointer states that are characterized by a large differential photon occupation.Following this mapping, we photodetect the resonator using the Josephson photomultiplier, which transitions between classically distinguishable flux states when cavity photon occupation exceeds a certain threshold.Our technique provides access to the binary outcome of projective quantum measurement at the millikelvin stage without the need for quantumlimited preamplification and thresholding at room temperature.We achieve raw single-shot measurement fidelity in excess of 98% across multiple samples using this approach in total measurement times under 500 ns.In addition, we show that the backaction and crosstalk associated with our measurement protocol can be mitigated by exploiting the intrinsic damping of the Josephson photomultiplier itself.
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depend on the quantity that is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrated this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures was observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.