Quantum limits to center-of-mass measurements

Vaughan, Timothy G.; Drummond, P. D.; Leuchs, Gerd

doi:10.1103/physreva.75.033617

Cited by 18 publications

(7 citation statements)

References 53 publications

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“…Mathematically, the difference between the predictions of the many-body and mean-field descriptions can be tracked down to the subtlety of performing the infinite-particle limit only after (and not before) the many-particle operator is evaluated. In comparison with the variance of an operator of a single particle, the variance of many-particle operators is a much richer quantity, also see [22][23][24][25] in this context. At the bottom line, the many-body and mean-field wave-functions themselves differ at the infinite-particle limit and, consequently, their overlap is always smaller than one and can become arbitrarily small [19,26].…”

Section: Introductionmentioning

confidence: 99%

Variance of an anisotropic Bose-Einstein condensate

et al. 2018

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The anisotropy of a trap potential can impact the density and variance of a Bose-Einstein condensate (BEC) in an opposite manner. We exemplify this effect for both the ground state and out-of-equilibrium dynamics of structureless bosons interacting by a long-range inter-particle interaction and trapped in a two-dimensional single-well potential. We demonstrate that even when the density of the BEC is, say, wider along the y direction and narrower along the x direction, its position variance can actually be smaller and momentum variance larger in the y direction than in the x direction. This behavior of the variance in a many-particle system is counterintuitive. It suggests using the variance as a tool to characterize the strength of correlations along the y and x directions in a trapped BEC.

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Section: Introductionmentioning

confidence: 99%

Variance of an anisotropic Bose-Einstein condensate

et al. 2018

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“…d) Concerning the experimental and theoretical limits put on the measurements of position (center of mass) of an atom, see Refs. [55,56]. In this case, the uncertainty of the localization (of the order of nanometers) is much bigger than the Compton wavelength of the atom itself!…”

Section: Discussionmentioning

confidence: 99%

On the transition from the quantum to the classical regime for massive scalar particles: A spatiotemporal approach

Lusanna

Pauri

2014

Eur. Phys. J. Plus

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If the classical structure of space-time is assumed to define an a-priori scenario for the formulation of the structure of quantum theory (QT), the coordinate representation of the solutions ψ( x, t) (ψ( x 1 , .., x N , t)) of the Schroedinger equation of a quantum system containing one (N ) massive scalar particle has a preferred status. It is then possible to perform a multipolar expansion of the density matrix ρ( x, t) = |ψ( x, t)| 2 (and more generally of the Wigner function) around a space-time trajectory x c (t) to be properly selected. A special set of solutions ψ EM W F ( x, t), named Ehrenfest monopole wave functions(EMWF), is characterized by the conditions that: (i) the quantum expectation value of the position operator coincides at any time with the searched classical trajectory, < ψ EM W F |ˆ x|ψ EM W F >= x c (t), and, (ii) Ehrenfest's theorem holds for the expectation values of the position and momentum operators. The first condition implies the vanishing of the 'dipole' term in the multipolar expansion of the density matrix with respect to such trajectory. Ehrenfest's theorem applied to EMWF leads then to a closed Newton equation of motion for the classical trajectory, where the effective force is the Newton force plus non-Newtonian terms (of order 2 or higher) depending on the higher multipoles of the probability distribution ρ. Note that the super-position of two EMWFs is not an EMWF, a result to be strongly hoped for, given the possible unwanted implications concerning classical spatial perception. These results can be extended to N particle systems and to relativistic quantum mechanics.Consequently, for the states of a quantum particle which are EMWF, we get the emergence of a corresponding classical 'effective' particle following a Newton-like trajectory in space-time.Note that this holds true in the standard framework of quantum mechanics, i.e. by assuming the validity of Born's rule and the individual system interpretation of the wave function (no ensemble interpretation). These results are valid without any approximation (like → 0, big quantum numbers,...). Moreover, we do not commit ourselves to any ontological interpretation of quantum theory (such as, e.g., the Bohmian one. It will be clear that our trajectories are not Bohm's trajectories). We will argue that, in substantial agreement with Bohr's viewpoint, the macroscopic description of the preparation, certain intermediate steps and the detection of the final outcome of experiments involving massive particles are dominated by these 'classical effective trajectories'.This approach can be applied to the point of view of de-coherence (in which positions turn out to be selected preferred robust bases) in the case of a diagonal reduced density matrix ρ red (an improper mixture) depending on the position variables of a massive particle and of a pointer. When both the particle and the pointer wave functions appearing in ρ red are EMWF, the expectation value of the particle and pointer position variables becomes a statistical average on a cl...

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“…[33], where it is shown that it is only possible to measure mutual relative positions of atoms. Regarding their absolute positions the best localization of atoms which can be realized is at the level of hundred of nanometers [34,35], much higher than the atom Compton wavelength.…”

Section: B Non-relativistic Casementioning

confidence: 99%

On relativistic entanglement and localization of particles and on their comparison with the nonrelativistic theory

Crater

Lusanna

2014

Int. J. Mod. Phys. A

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We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames as well of the open problems in particle localization at both levels. The solution of the problems of the relativistic center of mass, of the clock synchronization convention needed to define relativistic 3-spaces and of the elimination of the relative times in the relativistic bound states leads to a description with a decoupled non-local (non-measurable) relativistic center of mass and with only relative variables for the particles (single particle subsystems do not exist). We analyze the implications for entanglement of this relativistic spatial non-separability not existing in non-relativistic entanglement. Then we try to reconcile the two visions showing that also at the non-relativistic level in real experiments only relative variables are measured with their directions determined by the effective mean classical trajectories of particle beams present in the experiment. The existing results about the non-relativistic and relativistic localization of particles and atoms support the view that detectors only identify effective particles following this type of trajectories: these objects are the phenomenological emergent aspect of the notion of particle defined by means of the Fock spaces of quantum field theory.

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Quantum limits to center-of-mass measurements

Cited by 18 publications

References 53 publications

Variance of an anisotropic Bose-Einstein condensate

Variance of an anisotropic Bose-Einstein condensate

On the transition from the quantum to the classical regime for massive scalar particles: A spatiotemporal approach

On relativistic entanglement and localization of particles and on their comparison with the nonrelativistic theory

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