Geometric phase corrections on a moving particle in front of a dielectric mirror

Abstract

-We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the unitary geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and integrate over the vacuum field and the microscopic degrees of freedom of both the plate and the particle in order to calculate friction effects. We compute analytically and numerically the non-unitary geometric phase for the moving qubit under the presence of the quantum vacuum field and the dielectric mirror. We find a velocity dependence in the correction to the unitary geometric phase due to quantum frictional effects. We also show in which cases decoherence effects could, in principle, be controlled in order to perform a measurement of the geometric phase using standard procedures as Ramsey-like interferometry.Introduction. -A system can retain the information of its motion when it undergoes a cyclic evolution in the form of a geometric phase, which was first put forward by Pancharatman in optics [1] and later studied explicitly by Berry in a general quantal system [2]. Since the work of Berry, the notion of geometric phases has been shown to have important consequences for quantum systems. Berry demonstrated that quantum systems could acquire phases that are geometric in nature. He showed that, besides the usual dynamical phase, an additional phase related to the geometry of the space state is generated during an adiabatic evolution. Since then, great progress has been achieved in this field. Due to its global properties, the geometric phase is propitious to construct fault tolerant quantum gates. In this line of work, many physical systems have been investigated to realise geometric quantum computation, such as NMR (Nuclear Magnetic Resonance) [3], Josephson junction [4], Ion trap [5] and semiconductor quantum dots [6]. The quantum computation scheme for the geometric phase has been proposed based on the Abelian or non-Abelian geometric concepts, and the geometric phase has been shown to be robust against faults in the presence of some kind of external noise due to the geometric nature of Berry phase [7][8][9]. It was therefore seen that interactions play an important role in the realisation of some specific operations. As the gates operate

Towards detecting traces of non-contact quantum friction in the corrections of the accumulated geometric phase

“…3 also shows that the correction to the GP fits quadratically with u as can be seen in Ref. [36] for small tangential velocities. The phase-lag induced by the motion on the fluctuating dipole results in dynamical effects (noise and dissipation in equation (2)).…”

“…3 we show the correction to the phase δφ defined as the difference between φ g the total geometric phase and Correction to the GP fits quadratically with u as can be seen in Ref. [36] for small tangential velocities. Parameters used: ∆/ω pl = 0.9, Γ/ω pl = 0.1, ω0/ω pl = 0, N = 15, θ0 = 44.9 • .…”

“…The GP shift is manifested as a relative phase between components of a superposition of atomic states. In [36] some of us have proposed a very simplistic model with this idea, where a harmonic oscillator (the "atom") is coupled to an scalar field (as the "vacuum field") and the later is coupled to a mirror composed by a set of harmonic oscillators without dissipation and with an unique natural frequency. Therein the coupling considered was purely dephasing just for the sake of simplicity, far away of any real experimental consideration.…”

Geometry of quantum evolution in a nonequilibrium environment

“…Combining Eqs. (24) with (26), it indicates that the frequency shift s(t) induced by the environmental nonequilibrium feature also has a significant impact on the correction to the effective geometric phase.…”

Boundary-induced effect encoded in the corrections to the geometric phase acquired by a bipartite two-level system

“…It has also been suggested as a measure of the Unruh effect at lower accelerations [12][13][14]. Recently, it has even been proposed to track traces of quantum friction in the case of an atom coupled to a scalar quantum field, traveling at constant velocity at a fixed distance in front of a dielectric plate [15]. Another major concept in quantum physics happens to be that of entanglement, playing a central role in many novel quantum technologies [16,17].…”