Zero mode suppression of superluminal signals in light-matter interactions

Abstract

We show how two Unruh-DeWitt detectors that do not couple to the zero mode of a quantum field can exchange information faster than the speed of light. We analyze the specific cases of periodic and Neumann boundary conditions in flat spacetime with arbitrary spatial dimensions, and we show that the superluminal signal strength is only polynomially suppressed with the distance to the lightcone. Therefore, in any relativistic scenario modelling the light-matter interaction where a zero mode is present, particle detectors should explicitly couple to the zero mode. * e2tjoa@uwaterloo.ca † emartinmartinez@uwaterloo.ca 1 Note that in the context of algebraic quantum field theory (AQFT), sometimes this is known as a version of locality [22,30].

Impossible measurements require impossible apparatus

“…Finally it is worth mentioning that non-relativistic, non-local particle detector models are a very common tool and widely used for example in quantum field theory in curved spacetime and relativistic quantum information. Other authors have shown that coupling such a detector model to a finite number of field modes [2] or to all but the zero mode [20] leads to superluminal signalling. In view of our result, this is due to the nonlocality of such a coupling, whereas the detector model sketched at the end of [7] consequently does not signal superluminally.…”

The time traveler’s guide to the quantization of zero modes

“…It is known that quantization of a massless scalar field on a topologically closed spacetime and under certain boundary conditions can give rise to zero modes. A zero mode naturally arises when a massless scalar field is subject to periodic or Neumann boundary conditions, or when the background spacetime has toroidal topology in all spatial directions [26][27][28][29][30]. Zero modes are problematic because they do not admit a Fock representation, thus the physical ground state of the zero mode, and hence the full theory, is a priori ambiguous [26,27].…”

“…A zero mode naturally arises when a massless scalar field is subject to periodic or Neumann boundary conditions, or when the background spacetime has toroidal topology in all spatial directions [26][27][28][29][30]. Zero modes are problematic because they do not admit a Fock representation, thus the physical ground state of the zero mode, and hence the full theory, is a priori ambiguous [26,27]. For this reason zero modes are sometimes removed by hand [31][32][33][34][35], but such procedure leads to unacceptable causality violations and other issues [27,28].…”

“…Zero modes are problematic because they do not admit a Fock representation, thus the physical ground state of the zero mode, and hence the full theory, is a priori ambiguous [26,27]. For this reason zero modes are sometimes removed by hand [31][32][33][34][35], but such procedure leads to unacceptable causality violations and other issues [27,28]. Some reasonable regularization of the unphysical ground state of the zero mode, using squeezed vacuum of a quantum harmonic oscillator, has been proposed in [26][27][28] and how the choice of regularization impacts the dynamics was studied.…”

Open quantum systems and applications to the quantum information theory

“…Having an exactly solvable model allows us to demonstrate explicitly that this non-causal behavior is not an artifact of common approximations employed in such systems-for causality violation in Unruh-DeWitt detectors in a perturbative evaluation, see [62,63]. First, non-causality is not due to the choice of a factorizing initial condition, that was employed in the derivation of the density matrix propagator.…”