Modified uncertainty principle from the free expansion of a Bose–Einstein condensate

Castellanos, Elías; Escamilla-Rivera, Celia

doi:10.1142/s0217732317500079

Cited by 8 publications

(3 citation statements)

References 30 publications

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“…The representation (2.20), (2.21) may be used [19,[52][53][54][55][56][57] to derive the spectra of simple quantum mechanical systems whose dynamics is determined for example by central potentials. In such systems the Hamiltonian is of the form [53]…”

Section: Ii2 Three Dimensionsmentioning

confidence: 99%

Cosmological horizons, uncertainty principle, and maximum length quantum mechanics

Perivolaropoulos¹

2017

Phys. Rev. D

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The cosmological particle horizon is the maximum measurable length in the Universe. The existence of such a maximum observable length scale implies a modification of the quantum uncertainty principle. Thus due to non-locality of quantum mechanics, the global properties of the Universe could produce a signature on the behaviour of local quantum systems. A Generalized Uncertainty Principle (GUP) that is consistent with the existence of such a maximum observable length scale lmax is ∆x∆p ≥ 2 √ α. Using appropriate representation of the position and momentum quantum operators we show that the spectrum of the one dimensional harmonic oscillator becomesĒn = 2n + 1 + λnᾱ whereĒn ≡ 2En/ ω is the dimensionless properly normalized n th energy level,ᾱ is a dimensionless parameter withᾱ ≡ α /mω and λn ∼ n 2 for n 1 (we show the full form of λn in the text). For a typical vibrating diatomic molecule and lmax = c/H0 we findᾱ ∼ 10 −77 and therefore for such a system, this effect is beyond reach of current experiments. However, this effect could be more important in the early universe and could produce signatures in the primordial perturbation spectrum induced by quantum fluctuations of the inflaton field.

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Section: Ii2 Three Dimensionsmentioning

confidence: 99%

Cosmological horizons, uncertainty principle, and maximum length quantum mechanics

Perivolaropoulos¹

2017

Phys. Rev. D

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“…Analogs, i.e. physical systems governed by laws mathematically identical to those of the generalized quantum mechanics, were considered in the fields of optics and relativistic BECs [51][52][53][54][55]. The fact that non-paraxial quantum fluids enable the simulations of non-commutative quantum mechanics, and general relativistic effects, opens several possibilities for studying analogs of unexplored phenomena in the laboratory.…”

Section: Introductionmentioning

confidence: 99%

Simulating general relativity and non-commutative geometry by non-paraxial quantum fluids

Marcucci

Conti

2019

New J. Phys.

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We show that quantum fluids enable experimental analogs of relativistic orbital precession in the presence of non-paraxial effects. The analysis is performed by the hydrodynamic limit of the Schrödinger equation. The non-commutating variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is formally identical to the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton's theory. In our case, the corrections are due to the modified uncertainty principle. The results may enable novel relativistic analogs in the laboratory, also including sub-Planckian phenomenology.

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“…[33] Analogs, i.e., physical systems governed by laws mathematically identical to those of the generalized quantum mechanics, were considered in the fields of optics and relativistic Bose-Einstein condensates. [44][45][46][47][48] In this manuscript, we study the orbital precession of a quantum fluid (Figure 1a) due to the perturbation to quantum mechanics induced by quantum gravity and -more specifically -due to the additional kinetic terms that account for the generalized uncertainty principle as in Eq. ( 1).…”

Section: Introductionmentioning

confidence: 99%

Quantum-gravity-slingshot: orbital precession due to the modified uncertainty principle, from analogs to tests of Planckian physics with quantum fluids

Marcucci,

Conti

2018

Preprint

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Modified uncertainty principle and non-commutative variables may phenomenologically account for quantum gravity effects, independently of the considered theory of quantum gravity. We show that quantum fluids enable experimental analogs and direct tests of the modified uncertainty principle expected to be valid at the Planck scale. We consider a quantum clock realized by a long-lasting quantum fluid wave-packet orbiting in a trapping potential. We investigate the hydrodynamics of the Schrödinger equation encompassing kinetic terms due to Planck-scale effects. We study the resulting generalized mechanics and validate the predictions by quantum simulations. Wave-packet orbiting generates a continuous amplification of the quantum gravity effects. The non-commutative variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is strongly resembling the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton's theory. In our case, the corrections are due to the modified uncertainty principle. The results can be employed to emulate quantum gravity in the laboratory, or to realize human-scale experiments to determine bounds for the most studied quantum gravity models and probe Planckian physics.

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Modified uncertainty principle from the free expansion of a Bose–Einstein condensate

Cited by 8 publications

References 30 publications

Cosmological horizons, uncertainty principle, and maximum length quantum mechanics

Cosmological horizons, uncertainty principle, and maximum length quantum mechanics

Simulating general relativity and non-commutative geometry by non-paraxial quantum fluids

Quantum-gravity-slingshot: orbital precession due to the modified uncertainty principle, from analogs to tests of Planckian physics with quantum fluids

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