It is now well-established that photonic systems can exhibit topological energy bands; similar to their electronic counterparts, this leads to the formation of chiral edge modes whichcan be used to transmit light in a manner that is protected against back-scattering. Most topological photonic states are completely analogous to their electronic counterpart, as they are based on single-particle physics: the topological invariants and edge states are identical in both the bosonic and fermionic case. Here, we describe a new kind of topological photonic state which has no electronic analogue. In our system, a non-zero topological invariant guarantees the presence of a parametrically-unstable chiral edge mode in a system with boundaries, even though there are no bulk-mode instabilities. We show that by stabilizing these unstable edge modes via coupling waveguides, one realizes a topologically protected, quantum-limited travelling-wave parametric amplifier. The device is protected against both internal losses and back-scattering; the latter feature is in stark contrast to standard travelling wave amplifiers. We show that the unstable edge mode also naturally serves as a topologically-protected source for non-classical squeezed light.
We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement,and crucially, is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities, and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics free subspace). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circuit quantum electrodynamics.
Among the most exciting recent advances in the field of superconducting quantum circuits is the ability to coherently couple microwave photons in low-loss cavities to quantum electronicconductors (e.g.~semiconductor quantum dots or carbon nanotubes). These hybrid quantum systems hold great promise for quantum information processing applications; even more strikingly, they enable exploration of completely new physical regimes. Here we study theoretically the new physics emerging when a quantum electronic conductor is exposed to non-classical microwaves (e.g.~squeezed states, Fock states). We study this interplay in the experimentally-relevant situation where a superconducting microwave cavity is coupled to a conductor in the tunneling regime. We find the quantum conductor acts as a non-trivial probe of the microwave state; in particular, the emission and absorption of photons by the conductor is characterized by a non-positive definite quasi-probability distribution. This negativity has a direct influence on the conductance of the conductor.
We provide a thorough theoretical analysis of qubit state measurement in a setup where a driven, parametrically-coupled cavity system is directly coupled to the qubit, with one of thecavities having a weak Kerr nonlinearity. Such a system could be readily realized using circuit QED architectures. We demonstrate that this setup is capable in the standard linear-response regime of both producing a highly amplified output signal while at the same time achieving near quantum-limited performance: the measurement backaction on the qubit is near the minimal amount required by the uncertainty principle. This setup thus represents a promising route for performing efficient large-gain qubit measurement that is completely on-chip, and that does not rely on the use of circulators or complex non-reciprocal amplifiers.
We analyze the use of a driven nonlinear cavity to make a weak continuous
measurement of a dispersively-coupled qubit. We calculate the backaction
dephasing rate and measurement ratebeyond leading-order perturbation theory
using a phase-space approach which accounts for cavity noise squeezing.
Surprisingly, we find that increasing the coupling strength beyond the regime
describable by leading-order perturbation theory (i.e. linear response) allows
one to come significantly closer to the quantum limit on the measurement
efficiency. We interpret this behaviour in terms of the non-Gaussian photon
number fluctuations of the nonlinear cavity. Our results are relevant to recent
experiments using superconducting microwave circuits to study quantum
measurement.