Critical Phenomenon of a Consistent q-Deformed Squeezed State

Abstract

Within a self-consistent framework of q-deformed Heisenberg algebra and its equivalent framework of q-deformed boson commutation relations, which relate to the under-cutting phenomenon of Heisenberg's minimal uncertainty relation, special q-deformed squeezed states are constructed. Besides the similar local maximum squeezing as the one in the undeformed case, new strong squeezing appears when the amplitude of the related coherent state increases to large values. A critical phenomenon appears at a large value of the amplitude: the variance of one component of the quadrature of the light field approaches zero, but the variance of the corresponding conjugate quantity remains finite, which is a surprising deviation from Heisenberg's uncertainty relation. The qualitative character exposed by this q-squeezed state may provide some evidence about q-deformed effects in current experiments. *

Quantum limits to estimation of photon deformation

“…In particular, we address deformed coherent states, 14-16 thermal states, 17 and superposition cat-like states. 18 Our approach will be that of addressing the above classes of deformed states as families of states parametrized by a deformation-dependent parameter, and to employ tools from local quantum estimation theory to evaluate the ultimate bounds to precision in the estimation of this parameter by quantum-limited measurements. 19,20 In particular, we evaluate the quantum Fisher information (QFI) and the quantum signal-to-noise ratio (QSNR), and show that they are achieved by intensity measurements.…”

Perturbation foundation of q-deformed dynamics

“…In one approach the q-deformed quantum theory, as a possible modification of the ordinary quantum theory at space scale much smaller than 10 −18 cm, has attracted attention. In literature different frameworks of q-deformed quantum theories were established [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. We work in the framework of the q-deformed Heisenberg algebra developed in Refs.…”

“…[2,4], which is self-consistent and shows interesting physical content. In this framework characteristics of dynamics and uncertainty relations of q-deformed quantum mechanics are explored [1][2][3][4][5][6], [14][15][16][17][18][19][20].…”

q-Deformed dynamics and Virial theorem

“…In search for such possibility q-deformed quantum mechanics is a candidate. In literature different frameworks of qdeformed quantum mechanics were established [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The framework of the q-deformed…”

“…The q-deformed uncertainty relation undercuts the Heisenberg minimal uncertainty relation [15,16,18]. The non-perturbation energy spectrum of the q-deformed Schrödinger equation…”