Symmetry in Quantum Optics Models

Lamata, Lucas

doi:10.3390/sym11101310

Cited by 1 publication

(6 citation statements)

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“…namely that in which the elements of the fourth row and column vanish at t = 0 and then at any successive time. We remark that under such a restriction, the 3 × 3 block appearing in (38) can be interpreted as the initial density matrix of the nested qutrit.…”

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

“…Since the matrix (36) is the most common way of representing the initial density matrix of the two-spin system, we seek the conditions to be imposed on its elements so that its representation in the entangled basis (20) transparently exhibits the emergence of the nested qutrit, that is, assumes the form (38).…”

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

“…We emphasize that Equation (39) provides the recipe for writing an initial density matrix of two spins whose time evolution, in accordance with the mapping (19), simulates the dynamics of a qutrit with an initial density matrix given by the 3 × 3 block of (38), where the elements satisfy Equation (40). Therefore, we have the necessary and sufficient conditions for the emergence of a qutrit dynamics in the dipolar coupling of two qubits.…”

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

“…To better appreciate the above statement and exemplify its feasibility, it is interesting to investigate the compatibility between the two representations (36) and (38) when the former describes the simplest separable (factorable) state of the two-spin system, namely…”

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

“…Excluding (based on our defined goal) the mixed state of a singlet and a triplet in the class of density matrices (38), we obtain the additional condition:…”

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

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Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Belousov

Man’ko

Migliore

et al. 2022

Entropy

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We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole–dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.

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Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

“…Excluding (based on our defined goal) the mixed state of a singlet and a triplet in the class of density matrices (38), we obtain the additional condition:…”

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

See 3 more Smart Citations