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arXiv:1008.3363 · Physical Review B

Quantum nondemolition measurement of microwave photons using engineered quadratic interactions

Chunqing Deng, Jay Gambetta, Adrian Lupaşcu

Published Dec 14, 2010• 7 citations
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Abstract

We present a quantum electrical circuit with Josephson junctions formed of two anharmonic oscillators coupled with an interaction $g{\ensuremath{\gamma}}_{1}^{2}{\ensuremath{\gamma}}_{2}^{2}$, where ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$ are positionlike coordinates. This type of coupling allows the quantum nondemolition measurement of the energy of one oscillator by monitoring the frequency of the second oscillator. Despite the fundamental tradeoff between the coupling strength $g$ and maximum photon-storage capacity of the oscillators, it is possible to achieve high-fidelity detection of up to ten photons over time scale on the order of microseconds. We discuss the possibility of observing quantum jumps in the number of photons and related applications.

DOI
10.1103/physrevb.82.220505

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Inducing interactions between individual photons is key for photonic quantum information and studying many-body photon states. Superconducting circuits are well suited to combine strong interactions with low losses. Typically, microwave photons are stored in an LC oscillator shunted by a Josephson junction, where the zero-point phase fluctuations across the junction determine the strength and order of photon interactions. Most superconducting nonlinear oscillators operate with small phase fluctuations, where two-photon Kerr interactions dominate. In our experiment, we shunt a high-impedance LC oscillator with a dipole element favoring the tunneling of paired Cooper pairs. This leads to large phase fluctuations of 3.4, accessing a regime where transition frequencies shift non-monotonically with excitation number. From spectroscopy, we extract two-, three-, and four-photon interaction energies, all of similar strength and exceeding the photon loss rate. Our results open a new regime of high-order photon interactions in microwave quantum optics. In superconducting circuits, the nonlinearity of Josephson junctions mediates photon interactions, but they are typically dominated by two-photon processes. Here the authors observe multi-photon interactions in a superconducting circuit with Cooper-pair pairing, revealing a new regime of microwave quantum optics.
We consider making quantum nondemolition measurements on a harmonic oscillator by coupling it to an oscillator readout system using a four-wave-mixing interaction. The quantum nondemolition variable of interest appears as a nonlinear function of the number operator. It has the form ${\stackrel{^}{D}}_{1}(t)=cos(\ensuremath{\chi}{a}^{\ifmmode\dagger\else\textdagger\fi{}}at)$. A sequence of measurements of this operator may be made with completely predictable results. The possible use of this system to detect gravitational radiation is suggested.
Over the past decade, quantum coherent behavior has been observed in electrical circuits engineered to have discrete, individually addressable energy levels. These devices operate at cryogenic temperatures and microwave frequencies-conditions which permit the utilization of superconducting passive and active resonant circuits for measurement. The basic architecture of a quantum dispersive measurement consisting of a two level quantum bit coupled to a LC tank circuit is reviewed. Recent progress with this type of readout has led to the real time monitoring of a superconducting qubit with the observation of quantum jumps between energy levels.
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We analyze the detection of itinerant photons using a quantum nondemolition measurement. An important example is the dispersive detection of microwave photons in circuit quantum electrodynamics, which can be realized via the nonlinear interaction between photons inside a superconducting transmission line resonator. We show that the back action due to the continuous measurement imposes a limit on the detector efficiency in such a scheme. We illustrate this using a setup where signal photons have to enter a cavity in order to be detected dispersively. In this approach, the measurement signal is the phase shift imparted to an intense beam passing through a second cavity mode. The restrictions on the fidelity are a consequence of the quantum Zeno effect, and we discuss both analytical results and quantum trajectory simulations of the measurement process.
We propose a quantum nondemolition (QND) readout scheme for a superconducting artificial atom coupled to a resonator in a circuit QED architecture, for which we estimate a very high measurement fidelity without Purcell effect limitations. The device consists of two transmons coupled by a large inductance, giving rise to a diamond-shaped artificial atom with a logical qubit and an ancilla qubit interacting through a cross-Kerr-like term. The ancilla is strongly coupled to a transmission line resonator. Depending on the qubit state, the ancilla is resonantly or dispersively coupled to the resonator, leading to a large contrast in the transmitted microwave signal amplitude. This original method can be implemented with a state-of-the-art Josephson parametric amplifier, leading to QND measurements in a few tens of nanoseconds with fidelity as large as 99.9%.