The su(1,1)-like intensity-dependent Rabi model: A perturbative analysis of weak and strong-coupling regimes

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560010 ◽  
Author(s):  
Vittorio Penna ◽  
Francesco A. Raffa
Keyword(s):  
Strong Coupling ◽  
Photon Number ◽  
Single Mode ◽  
Strong Coupling Regime ◽  
Model Parameters ◽  
Energy Eigenvalues ◽  
First Case ◽  
Coupling Case ◽  
Rabi Model ◽  
Almost Continuous

We present a perturbative analysis of a Rabi model where the coupling between the quantized single-mode electromagnetic field and the two-level atom depends on the field intensity. Upon modeling the matter–radiation coupling through the Holstein–Primakoff realization of algebra su(1,1), we evaluate first- and second-order eigenenergies and eigenstates both in the weak-coupling regime (atom transition frequency smaller than the coupling strength) and in the strong-coupling regime. In the first case, among various effects, we observe a quadratic dependence on the photon number of energy eigenvalues and the possible formation of level doublets. In the strong-coupling case, the perturbative analysis becomes considerably complex due to the su(1,1)-valued form of the unperturbed Hamiltonian. The critical condition for the transition to an almost continuous spectrum is found in terms of the model parameters.

scholarly journals On the 2-mode and k-photon quantum Rabi models

2017 ◽  
Vol 29 (04) ◽  
pp. 1750013 ◽  
Author(s):  
Yao-Zhong Zhang
Keyword(s):  
Hilbert Spaces ◽  
Differential Operators ◽  
Entire Functions ◽  
Wave Functions ◽  
Model Parameters ◽  
Energy Eigenvalues ◽  
Rabi Model ◽  
Transcendental Equations ◽  
Strength Formula ◽  
Bargmann Hilbert Space

By mapping the Hamiltonians of the 2-mode and 2-photon Rabi models to differential operators in suitable Hilbert spaces of entire functions, we prove that the two models possess entire and normalizable wave functions in the Bargmann–Hilbert spaces only if the frequency [Formula: see text] and coupling strength [Formula: see text] satisfy certain constraints. This is in sharp contrast to the quantum Rabi model for which entire wave functions always exist. For model parameters fulfilling the aforesaid constraints, we determine transcendental equations whose roots give the regular energy eigenvalues of the models. Furthermore, we show that for [Formula: see text], the [Formula: see text]-photon Rabi model does not possess wave functions which are elements of the Bargmann–Hilbert space for all non-trivial model parameters. This implies that the [Formula: see text] case is not diagonalizable, unlike its RWA cousin, the [Formula: see text]-photon Jaynes–Cummings model which can be completely diagonalized for all [Formula: see text].

Quantum speed-up dynamical crossover in open systems

2017 ◽  
Vol 15 (04) ◽  
pp. 1750027
Author(s):  
W.-J. Wu ◽  
K. Yan ◽  
Y.-Q. Xie ◽  
Yinzhong Wu ◽  
Xiang Hao
Keyword(s):  
Decay Rate ◽  
Strong Coupling ◽  
Open Systems ◽  
Spontaneous Decay ◽  
Strong Coupling Regime ◽  
Energy Feedback ◽  
Potential Capacity ◽  
Coupling Case ◽  
Acceleration And Deceleration ◽  
Dynamical Crossover

We put forward a measure for evaluating quantum speed limit for arbitrary mixed states of open systems by means of trace distance. Compared with some present measures, it can provide an optimal bound to the speed of the evolution. The dynamical crossover from no speedup region to speedup region happens during the spontaneous decay of an atom. The evolution is characteristic of the alternating behavior between quantum acceleration and deceleration in the strong coupling case. Under the condition of detuning, the evolution can be initially accelerated and then decelerated to a normal process either in the weak or strong coupling regime. In accordance with the uncertainty relation, we demonstrate that the potential capacity for quantum speedup evolution is closely related to the energy feedback from the reservoir to the system. The negative decay rate for the evolution results in the speedup process where the photons previously emitted by the atom are reabsorbed at a later time. The values of the spontaneous decay rate become positive after a long enough time, which results in the evolution with no speedup potential.

scholarly journals Double Rabi splitting in methylene blue dye-Ag nanocavity

Nanophotonics ◽  
2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiaobo Han ◽  
Fang Li ◽  
Zhicong He ◽  
Yahui Liu ◽  
Huatian Hu ◽  
...  
Keyword(s):  
Methylene Blue ◽  
Strong Coupling ◽  
Single Mode ◽  
Blue Dye ◽  
Strong Coupling Regime ◽  
Methylene Blue Dye ◽  
Dye Molecules ◽  
Rabi Splitting ◽  
Ag Nanocube ◽  
Multi Mode

Abstract We demonstrate a double Rabi splitting totaling 348 meV in an Ag nanocavity embedding of methylene blue (MB) dye layer, which is ascribed to the equilibrium state of monomer and dimer coexistence in MB dye. At low dye concentration, the single-mode strong coupling between the monomer exciton in MB dye and the Ag nanocavity is observed. As the dye concentration is increased, three hybridized plexciton states are observed, indicating a double Rabi splitting (178 and 170 meV). Furthermore, the double anti-crossing behavior of the three hybrid states is observed by tuning the Ag nanocube size, which validates the multi-mode strong coupling regime. It shows clear evidence on the diverse exciton forms of dye molecules, both of which can interact with plasmonic nanocavity, effectively. Therefore, it provides a good candidate for realizing the multi-mode strong coupling.

Improving entanglement of two atoms in strong coupling regime

2016 ◽  
Vol 30 (07) ◽  
pp. 1650033
Author(s):  
Hui Liu ◽  
Qing Yang ◽  
Ming Yang ◽  
Zhuoliang Cao
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Strong Coupling ◽  
Single Mode ◽  
Strong Coupling Regime ◽  
Quantum Jump ◽  
Rotating Wave Approximation ◽  
Wave Approximation ◽  
Rotating Wave ◽  
Single Mode Cavity

We consider a model of two identical atoms coupled to a single-mode cavity. When in atom-field strong coupling regime, the entanglement of the two atoms with spontaneous emission should be investigated beyond rotating-wave approximation (RWA). In order to improve the entanglement of the two atoms, some typical feedback based on quantum-jump are attempted to impose on the atoms. The result of numerical simulations shows that an appropriate feedback control can improve the entanglement.

scholarly journals Analog quantum simulation of the Rabi model in the ultra-strong coupling regime

2017 ◽  
Vol 8 (1) ◽  
Author(s):  
Jochen Braumüller ◽  
Michael Marthaler ◽  
Andre Schneider ◽  
Alexander Stehli ◽  
Hannes Rotzinger ◽  
...  
Keyword(s):  
Strong Coupling ◽  
Quantum Simulation ◽  
Strong Coupling Regime ◽  
Rabi Model
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