Entanglement generation in relativistic cavity motion

Abstract

We analyse particle creation and mode mixing for a quantum field in an accelerated cavity, assuming small accelerations but allowing arbitrary velocities, travel times and travel distances, and in particular including the regime of relativistic velocities. As an application, we identify a desktop experimental scenario where the mode mixing resonance frequency in linear sinusoidal motion or in uniform circular motion is significantly below the particle creation resonance frequencies of the Dynamical Casimir Effect, and arguably at the threshold of current technology. The mode mixing acts as a beamsplitter quantum gate, experimentally detectable not only via fluxes or particle numbers but also via entanglement generation.

Fifty Years of the Dynamical Casimir Effect

“…Various aspects of the problem of entanglement in systems with moving mirrors (or their analogs) were considered in Refs. [143,144,333,346,361,363,[524][525][526][527][528][529][530][531][532][533][534][535][536][537][538][539]. The quantum discord in the DCE was the subject of studies [333,540].…”

Scalar, spinor, and photon fields under relativistic cavity motion

“…In this section we address a real scalar field of strictly positive mass in (1 + 1)-dimensional Minkowski spacetime, with Dirichlet boundary conditions at the cavity walls. While the core results can be found in earlier short format papers [12][13][14]19], our purpose here is to be sufficiently self-contained to allow a direct comparison to the Maxwell field analysis in Sec. V.…”

“…While this small acceleration formalism overlaps in part with situations covered by the small distance approximations often considered in the DCE literature [6,7], and by other approximation schemes [15,16], its novelty is in the ability to accommodate relativistic velocities in a systematic fashion. Applications to quantum information tasks in relativistic or potentially relativistic contexts have been analysed in [12][13][14][17][18][19][20][21][22][23]. In particular, the formalism is applicable to a cavity whose motion is implemented by superconducting quantum interference device (SQUID) circuits without mechanically moving parts [23].…”

“…The cavity is assumed to be mechanically rigid, as seen in its instantaneous rest frame, and the acceleration is assumed to be small in magnitude, compared with the inverse linear dimensions of the cavity. Under these assumptions the evolution of a scalar field in the cavity can be solved in a recently developed formalism that treats the acceleration perturbatively but allows the velocities, the travel times, and the travel distances to remain arbitrary, and in particular allows the velocities to become relativistic [12][13][14]. For acceleration with constant direction, the notion of a relativistic rigid body can be implemented to all orders in the perturbative expansion, and for acceleration with varying direction, the formalism has been developed to first order in the * pmxnf@nottingham.ac.uk † pmxal3@nottingham.ac.uk ‡ jorma.louko@nottingham.ac.uk acceleration without relativistic ambiguities [13].…”

“…A fourth purpose is to give a proper justification to certain technical properties that have been stated and utilised in earlier papers [12][13][14][17][18][19][20][21][22][23]. In particular, we explain how the direction of the acceleration comes to be encoded in the Bogoliubov coefficient formulas.…”