Abstract There seems to exist agreement about the fact that inflation squeezes the quantum state of cosmological perturbations and entangles modes with wavenumbers k⟶ and - k⟶ . Paradoxically, this result has been used to justify both the classicality as well as the quantumness of the primordial perturbations at the end of inflation. We reexamine this question and point out that the definition of two-mode squeezing of the modes k⟶ and - k⟶ used in previous work rests on choices that are only justified for systems with time-independent Hamiltonians and finitely many degrees of freedom. We argue that for quantum fields propagating on generic time-dependent Friedmann-Lemaître-Robertson-Walker backgrounds, the notion of squeezed states is subject to ambiguities, which go hand in hand with the ambiguity in the definition of particles. In other words, we argue that the question “does the cosmic expansion squeeze and entangle modes with wavenumbers k⟶ and - k⟶ ?” contains the same ambiguity as the question “does the cosmic expansion create particles?”. When additional symmetries are present, like in the (quasi) de Sitter-like spacetimes used in inflationary models, one can resolve the ambiguities, and we find that the answer to the question in the title turns out to be in the negative. We further argue that this fact does not make the state of cosmological perturbations any less quantum, at least when deviations from Gaussianity can be neglected.
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Resolving ambiguities of the mode truncation in cavity quantum electrodynamics
This work provides the fundamental theoretical framework for few-mode cavity quantum electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonians under the photonic mode truncation. We first propose a general framework to resolve ambiguities for an arbitrary truncation in a given gauge. Then, we specifically consider the case of mode truncation, deriving gauge invariant expressions for both the Coulomb and dipole gauge Hamiltonians that naturally reduce to the commonly used single-mode Hamiltonians when considering a single-mode truncation. We finally provide the analytical and numerical results of both atomic and molecular model systems coupled to the cavity to demonstrate the validity of our theory.
more » « less- Award ID(s):
- 2124398
- NSF-PAR ID:
- 10368704
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Letters
- Volume:
- 47
- Issue:
- 6
- ISSN:
- 0146-9592; OPLEDP
- Page Range / eLocation ID:
- Article No. 1446
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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