Touching from a distance

Abstract

Entanglement is one of the defining properties that distinguishes quantum systems from their classical counterparts. It refers to correlations between measurement outcomes on distinct (and potentially distant) degrees of freedom of a system that are stronger than those found in any classical experiment. Quantum entanglement is the key resource that enables the dramatic speedup of calculations in a quantum computer, as well as various other quantum information processing tasks. In a paper appearing in Physical Review Letters[1], Haohua Wang and co-workers at the University of California, Santa Barbara, US, Zheijiang University, China, and NEC Corporation, Japan, have experimentally demonstrated entanglement between two spatially separated oscillating electrical circuits. This experiment represents the latest step by these researchers towards the engineering of large scale networks of controlled, entangled systems, which might be useful as quantum computers [2], or for engineering new states of quantum matter [3, 4]. Harmonic oscillators would seem to be ideal building blocks for constructing highly entangled states. The harmonic oscillator is a particularly well studied exemplar: the classical physics of harmonic oscillators—such as a mass accelerated by the linear restoring force provided by a spring—is understood by high school physics students, whereas the quantum harmonic oscillator is one of the first systems to be dealt with in undergraduate quantum mechanics courses. The quantum dynamics of a harmonic oscillator can be solved exactly, and such solutions are often the starting point in the understanding of quantum field theory. Harmonic oscillators are ubiquitous in physics, and many realizations of such oscillators can be found, ranging from mechanical systems, electrical circuits, and lattice vibrations to elementary excitations of the electromagnetic field (photons). In the context of the experiment carried out by Wang et al., each harmonic oscillator consists of a coplanar waveguide resonator—equivalent to a circuit comprising a capacitor and an inductor (see Fig. 1). This resonator is superconducting at low temperature and can store excitations for a long time (in other words, it takes a relatively long time for excitations to decay—around 3 μs). Excitations of this circuit can be thought of as photons—excitations of the electromagnetic field associated with the circuit elements. Unfortunately, the simplicity of such harmonic oscillators means that a quantum system consisting solely of linearly coupled oscillators (that is, where the Hamiltonian contains coupling terms that are, at most, bilinear in the coordinate or conjugate momentum of each oscillator) is insufficient for many quantum information processing tasks. Such linear systems are not capable of implementing arbitrary quantum algorithms [5] (unless augmented with additional resources, such as single photon sources or photon-counting detectors [6]). Driving a harmonic oscillator with a classical oscillating field only allows the preparation of a restricted class of states, known as coherent states, and with only linear couplings between oscillators, it is not possible to transform such coherent initial states into entangled states of multiple oscillators. One can gain some insight into this restriction by considering the spectrum of a quantum harmonic oscillator: all the energy levels of the oscillator are equally spaced, and so it is not possible to address resonant transitions between a pair of states without also driving transitions between all other states. Wang et al.’s experiment overcomes these limitations with the inclusion of nonlinear circuit elements: each oscillator is coupled to a superconducting phase qubit, so called because the quantum information is represented by the phase difference between the supercon-