Spontaneous Casimir Effect

The dynamical Casimir effect predicts that vacuum amplification effects, resulting in the creation of real particles out of vacuum fluctuations, are induced by rapidly modulating the boundary conditions of a quantum field. Here we show that a spontaneous release of virtual photons from the quantum vacuum can occur in a quantum optical system in the ultrastrong coupling regime. In contrast to the dynamical Casimir effect and other pair creation mechanisms, this phenomenon does not require external forces or time dependent parameters. It resembles the production of particles during the early universe expansion induced by the decay of a false vacuum according to inflationary cosmology 1 ar X iv :1 21 0. 23 67 v1 [ qu an tph ] 8 O ct 2 01 2 The dynamical Casimir effect [3] has been recently experimentally realized in a superconducting circuit by modulating the inductance of a quantum interference device at high frequencies [4]. Other proposed vacuum amplification mechanisms [1], as the Schwinger process [12] and the Hawking radiation [13], require the presence of huge external fields or, as the Unruh effect, the presence of a rapidly nonuniformly accelerating observer [14], and have yet to be observed. The here described spontaneous release of virtual photon pairs in the absence of any external drive or observer acceleration resembles the particle production during the universe expansion predicted by modern inflationary cosmology. According to this theory, a scalar field starting in the false vacuum state eventually decays, and the energy that had been locked in it is released to form a hot, uniform soup of particles, which is the assumed starting point of the traditional big bang theory [11]. The Hamiltonian of a realistic atom-cavity system contains so-called counter-rotating terms allowing the simultaneous creation or annihilation of an excitation in both atom and cavity mode. These terms can be safely neglected for small coupling rates ΩR (rotatingwave approximation). However, when ΩR becomes comparable to the cavity resonance frequency of the emitter or the resonance frequency of the cavity mode, the counter-rotating terms are expected to manifest, giving rise to exciting effects in cavity QED [6, 15, 16]. This ultrastrong-coupling regime is difficult to reach in quantum-optical cavity QED, but was recently realized in a variety of solid-state quantum systems [5–10]. Such regime is challenging from a theoretical point of view as the total number of excitations in the cavityemitter system is not preserved, even though its parity is [16]. It has been shown that, in the ultrastrong coupling regime, the quantum optical master equation fails to provide the correct description of the system’s interaction with reservoirs [17]. Moreover quantum optical normal order correlation functions fail to describe photodetection experiments for such systems [18, 19]. Specifically, for a single mode resonator, the photon rate that can be detected by a photoabsorber is no more proportional to 〈a†(t)a(t)〉 (where a and a† are the photon destruction and creation operators) but to 〈X−(t)X+(t)〉, where X(t) is the positive frequency component of the quadrature operator X(t) = a(t) + a†(t) [19]. The most puzzling property of these systems is that their ground state is a squeezed vacuum containing correlated pairs of cavity photons [20]. The photon pairs in the ground state |0̃〉 are, however, virtual and cannot be detected [21], being 〈0̃|X−(t)X+(t)|0̃〉 = 0 [19]. Otherwise, an observation of a stream of photons from such