General superposition states associated to the rotational and inversion symmetries in the phase space

Abstract

The general quantum superposition states containing the irreducible representation of the n-dimensional groups associated to the rotational symmetry of the n-sided regular polygon i.e., the cyclic group (C n ) and the rotational and inversion symmetries of the polygon, i.e., the dihedral group (D n ) are defined and studied. It is shown that the resulting states form an n-dimensional orthogonal set of states which can lead to the finite representation of specific systems. The correspondence between the symmetric states and the renormalized states, resulting from the selective erasure of photon numbers from an arbitrary, noninvariant initial state, is also established. As an example, the general cyclic Gaussian states are presented. The presence of nonclassical properties in these states as subpoissonian photon statistics is addressed. Also, their use in the calculation of physical quantities as the entanglement in a bipartite system is discussed.

Mesoscopic quantum superposition states of weakly-coupled matter-wave solitons

“…for θ = 0, respectively. Notice, if we change the sign of tunneling rate, κ, the shift of phase θ by π is expected for (27), (28).…”

“…From fundamental point of view, BJJ-devices may form macroscopic SC-states [26]. Some recent results associated with symmetry (rotational and inversion) are obtained for superposition states in [27,28]. Practically, BJJ quantum features are promising for realization of macroscopic quantum computation [29,30], as well as for quantum metrology and sensing purposes [31].…”

Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States

“…There exist different representations of quantum states [ 39 , 40 , 41 , 42 , 43 , 44 ], and among them, the probability tomographic representation is of particular interest. In this representation, e.g., one-mode photon states are identified with symplectic tomograms [ 45 ], which correspond to the conditional probability distribution of the photon quadrature , to be measured in a reference frame with parameters and .…”

“…There exist different representations of quantum states [39][40][41][42][43][44], between them the probability tomographic representation is of particular interest. In this representation, e.g., one-mode photon Figure 2: Time evolution for the covariances (a) σ p 1 p 1 σ q 1 q 1 (dashed), and σ p 2 p 2 = σ q 2 q 2 (gray), (b) the covariances σ p 1 p 2 (black), σ p 1 q 2 (black dashed), σ p 2 q 1 (black dot-dashed), and σ q 1 q 2 (gray), (c) det σ 1 = det σ 2 for the subsystems (black) and the time dependence of the mean value Ĥ (t) (gray).…”

Gravito-diamagnetic forces for mass independent large spatial superpositions

“…Creating large spatial superposition states on a macroscopic scale represents a cutting-edge frontier in contemporary quantum research, intersecting theoretical exploration with experimental ingenuity. This pursuit holds significant promise for testing the foundational principles of quantum mechanics in the presence of gravity [1][2][3][4][5], investigating the equivalence principle [6,7], realizing a Crystallized Schrödinger cat states [8][9][10], placing bounds on decoherence mechanisms [11][12][13][14][15][16][17], and exploring applications in quantum sensors [18][19][20], the detection of gravitational waves [19], and the probing of a potential fifth force [21].…”