Invertibility of quantum-mechanical control systems

George T. Stamatiou, Kostas Magoutis

Hamad Ali, Abdul Basit, Zhao Ying‐jie

ABSTRACT Hybrid optomechanical systems that combine a cavity field, mechanical motion, and intracavity atomic media offer a versatile platform for engineering normal‐mode structure and macroscopic quantum correlations. Most atom‐assisted systems rely on passive absorbing media, leaving the role of an inverted ensemble acting as a resonant intracavity gain element largely unexplored. Here, we investigate a driven optomechanical cavity containing a movable mirror and two resonant atomic ensembles, one prepared in its ground state and the other inverted, thereby realizing a combined absorptive–amplifying intracavity response. We find that the inverted ensemble acts as an active control resource: tuning the gain coupling reshapes the hybrid‐mode structure and produces resolved normal‐mode peaks in both the mechanical and optical spectra, while the absorbing ensemble independently sets the mode linewidths and relative peak amplitudes. The coupling parameters control and redistribute the bipartite and tripartite Gaussian entanglement shared among the optical, mechanical, and atomic modes, with the mechanical thermal occupation setting the robustness of the correlations. Formulated with experimentally feasible parameters of existing strong‐coupling optomechanics, the scheme provides a tunable route to controlling normal‐mode splitting and quantum correlations in hybrid quantum systems.

En-Bing Lin

Manoj Kumar

Bogdan Mielnik, Arthur P. Ramirez, Piotr Kielanowski +4 more

A possible techniques to invert the free evolution in the Schrödinger’s quantum mechanics are presented and their pertinence to more general control problems is discussed. A new sense of the traditional Strutt diagram is exhibited.

Frank Gaitan

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\ensuremath{\varphi}(t)$ at the same time that it is inverted. For polynomial twist, $\ensuremath{\varphi}(t)\ensuremath{\sim}{\mathrm{Bt}}^{n}.$ We show that for $n>~3,$ multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength B, which can be used to control the time separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wave function. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum controlled-NOT and NOT gates is discussed.