Exploiting Kerr cross nonlinearity in circuit quantum electrodynamics for nondemolition measurements

Abstract

We propose a scheme for dispersive readout of stored energy in one mode of a nonlinear superconducting microwave ring resonator by detection of the frequency shift of a second mode coupled to the first via a Kerr nonlinearity. Symmetry is used to enhance the device responsivity while minimizing self nonlinearity of each mode. Assessment of the signal to noise ratio indicates that the scheme will function at the single photon level, allowing quantum non-demolition measurement of the photon number state of one mode. Experimental data from a simplified version of the device demonstrating the principle of operation are presented. PACS: 84.40.Dc, 85.25.Am

Engineering Dissipative Channels for Realizing Schrödinger Cats in SQUIDs

“…Our proposal makes use of non-linearly coupled electromagnetic fields and SQUIDs. Such quantum electrodynamic circuits have already been investigated in the context of weak non-demolition measurement (Deng et al, 2010;Kumar and DiVincenzo, 2010). One example comprises two microwave superconducting resonators coupled via a SQUID, which in addition to a cross Kerr effect also manifests two-photon conversion terms if the cavities are resonant (Kumar and DiVincenzo, 2010).…”

“…Such quantum electrodynamic circuits have already been investigated in the context of weak non-demolition measurement (Deng et al, 2010;Kumar and DiVincenzo, 2010). One example comprises two microwave superconducting resonators coupled via a SQUID, which in addition to a cross Kerr effect also manifests two-photon conversion terms if the cavities are resonant (Kumar and DiVincenzo, 2010). Such systems can be quantized (Everitt et al, 2001a,b;Stiffell et al, 2005;Wallquist et al, 2006) and with a suitable arrangement and choice of circuit parameters can be reduced (Wielinga and Milburn, 1993;Santamore et al, 2004) to the form of a double well system subject to a two-photon absorbing environment (see Section 4 for details).…”

“…There are a number of models (Deng et al, 2010;Kumar and DiVincenzo, 2010) whereby two microwave superconducting cavities can be non-linearly coupled using SQUIDs. We will base our discussion on Kumar and DiVincenzo (2010).…”

“…We note that there already exist schemes for realizing non-classical states via engineered dissipative channels (Amico et al, 2008;Diehl et al, 2008;Kraus et al, 2008;Schirmer and Wang, 2010;Ticozzi et al, 2010;Zhang et al, 2010;Busch et al, 2011;Pechen, 2011;Scully et al, 2011;Chen et al, 2012;Ticozzi and Viola, 2012;Yamamoto, 2012;Ikeda and Yamamoto, 2013) as well as a number of experimental realizations (Barreiro et al, 2011;Krauter et al, 2011;Leghtas et al, 2013). We also note that SQUIDs are an ideal candidate system for realizing this protocol as they have already been shown able to support appropriate quantum states (Nakamura et al, 1999;Friedman et al, 2000;Grajcar et al, 2004;Il'Ichev et al, 2004) and, as we shall later show, existing circuit designs can be used to engineer an environment with the suitable characteristics (Deng et al, 2010;Kumar and DiVincenzo, 2010).…”

Uniform phase modulation via control of refractive index in a thermal atom vapor with vanishing diffraction or absorption

“…In order to achieve such phase shifts, there have been extensive studies by utilizing nonlinear effects enhanced by quantum coherences and interferences. For example, self- [6,7] or cross- [8][9][10][11] phase modulation based on Kerr effect have been proposed using electromagnetically induced transparency (EIT) [12][13][14][15], spontaneously generated coherences [16] or active Raman gain [17,18] media, not only in gaseous-phase such as atomic alkali atoms, but also in solid-state media including optical fibers [3,19,20], quantum wells [21,22], and superconducting qubits [23][24][25]. Several schemes have been experimentally tested in cold [2, 11,26] or thermal atomic systems [6,10,27,28], where small nonlinear phase shifts up to the order of one radian are achieved.…”