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arXiv:2306.10573

Manifestation of strong and ultra-strong coupling in high-order correlation function

Anton S. Belashov, E. S. Andrianov, A. A. Zyablovsky

Published Jun 18, 2023• 0 citations
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Abstract

Strong and ultra-strong coupling in "cavity - single atom" system are of great interest for both fundamental and applied physics. It is considered that the increase in the coupling strength between a cavity mode and an atom leads, first, to transition from weak to strong coupling and, second, to ultra-strong coupling regime. In this letter, we refute this common opinion and demonstrate that the transitions between the coupling regimes occur in different sequence for the correlations' functions of different orders. We show that for n-th order correlations' functions, the transition to the strong coupling regime requires the coupling strength approximately by $n^{2/3}$ times greater than the one for first order correlations' functions. In contrast, the transition to the ultra-strong coupling regime manifests in the dynamics of n-th order correlations' functions at the less coupling strength than in the dynamics of first order correlations' functions. As a result, there is the order of correlations' functions, above which the increase in the coupling strength leads, first, to the transition from the weak coupling first to the ultra-strong coupling regime, and second to the strong coupling regime. We argue that the measurement of high orders correlations' functions makes it possible to observe the ultra-strong coupling in "cavity mode - single atom" when the coupling strength is much less than one tenth of the oscillation frequency.

DOI
10.48550/arxiv.2306.10573

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Strong and ultra-strong coupling in "cavity - single atom" system are of great interest for both fundamental and applied physics. It is considered that the increase in the coupling strength between a cavity mode and an atom leads, first, to transition from weak to strong coupling and, second, to ultra-strong coupling regime. In this letter, we refute this common opinion and demonstrate that the transitions between the coupling regimes occur in different sequence for the correlations' functions of different orders. We show that for n-th order correlations' functions, the transition to the strong coupling regime requires the coupling strength approximately by n2/3n^{2/3}n2/3 times greater than the one for first order correlations' functions. In contrast, the transition to the ultra-strong coupling regime manifests in the dynamics of n-th order correlations' functions at the less coupling strength than in the dynamics of first order correlations' functions. As a result, there is the order of correlations' functions, above which the increase in the coupling strength leads, first, to the transition from the weak coupling first to the ultra-strong coupling regime, and second to the strong coupling regime. We argue that the measurement of high orders correlations' functions makes it possible to observe the ultra-strong coupling in "cavity mode - single atom" when the coupling strength is much less than one tenth of the oscillation frequency.
Strong and ultra-strong coupling in a “cavity–single atom” system is of great interest for both fundamental and applied physics. It is considered that the increase in the coupling strength between a cavity mode and an atom leads, first, to transition from weak to strong coupling and, second, to the ultra-strong coupling regime. In this paper, we refute this common opinion and demonstrate that the transitions between the coupling regimes occur in different sequences for the correlation functions of different orders. We show that for n-th order correlation functions, the transition to the strong coupling regime requires a coupling strength approximately n2/3 times greater than the one for first order correlation functions. In contrast, the transition to the ultra-strong coupling regime manifests in the dynamics of n-th order correlation functions at less coupling strength than in the dynamics of first order correlation functions. As a result, the measurement of high-order correlation functions makes it easier to observe the ultra-strong coupling in “cavity mode–single atom.”
Abstract Single atoms coupled to a cavity offer unique opportunities as quantum optomechanical devices because of their small mass and strong interaction with light. A particular regime of interest in optomechanics is that of ‘single-photon strong coupling’, where motional displacements on the order of the zero-point uncertainty are sufficient to shift the cavity resonance frequency by more than its linewidth. In many cavity QED platforms, however, this is unfeasible due to the large cavity linewidth. Here, we propose an alternative route in such systems, which instead relies on the coupling of atomic motion to the much narrower cavity-dressed atomic resonance frequency. We discuss and optimize the conditions in which the scattering properties of single photons from the atom-cavity system become highly entangled with the atomic motional wave function. We also analyze the prominent observable features of this optomechanical strong coupling, which include a per-photon motional heating that is significantly larger than the single-photon recoil energy, as well as mechanically-induced oscillations in time of the second-order correlation function of the emitted light. This physics should be realizable in current experimental setups, such as trapped atoms coupled to photonic crystal cavities, and more broadly opens the door to realizing qualitatively different phenomena beyond what has been observed in optomechanical systems thus far.
The quantum dynamics of a strongly driven, strongly coupled single-atom-cavity system is studied by evaluating time-dependent second- and third-order correlations of the emitted photons. The coherent energy exchange, first, between the atom and the cavity mode, and second, between the atom-cavity system and the driving laser, is observed. Three-photon detections show an asymmetry in time, a consequence of the breakdown of detailed balance. The results are in good agreement with theory and are a first step towards the control of a quantum trajectory at larger driving strength.
We explore the role of quantum fluctuations in the strong-coupling limit of the dissipative Jaynes–Cummings oscillator driven on resonance. For weak excitation, we derive analytical expressions for the spectrum and the intensity correlation function for the photons scattered by the two-state atom coupled to the coherently driven cavity mode. We do so by writing down a birth–death process adding the higher orders in the excitation strength needed to go beyond the pure-state factorization, following the method introduced in Carmichael (2008). Our results for the first and second-order correlation functions are complemented by the numerical investigation of the waiting-time distribution for the photon emissions directed sideways, and the comparison with ordinary resonance fluorescence. To close out our discussion, we increase the driving field amplitude and approach the critical point organizing a second-order dissipative quantum phase transition by depicting the excitation pathways in the intracavity field distribution for a finite system size.
A major trend within the field of cavity QED is to boost the interaction strength between the cavity field and the atomic internal degrees of freedom of the trapped atom by decreasing the mode volume of the cavity. In such systems, it is natural to achieve strong atom-cavity coupling, where the coherent interaction strength exceeds the cavity linewidth, while the linewidth exceeds the atomic trap frequency. While most work focuses on coupling of photons to the internal degrees of freedom, additional rich dynamics can occur by considering the atomic motional degree of freedom as well. In particular, we show that such a system is a natural candidate to explore an interesting regime of quantum optomechanics, where the zero-point atomic motion yields a cavity frequency shift larger than its linewidth (so-called single-photon optomechanical strong coupling), but simultaneously where the motional frequency cannot be resolved by the cavity. We show that this regime can result in a number of remarkable phenomena, such as strong entanglement between the atomic wave function and the scattering properties of single incident photons, or an anomalous mechanism where the atomic motion can significantly heat up due to single-photon scattering, even if the atom is trapped tightly within the Lamb-Dicke limit.
An ultra-strong coupling regime takes place in a compound system when a coupling strength between the subsystems exceeds one-tenth of the system eigenfrequency. It transforms into a deep-strong coupling regime when the coupling strength exceeds the system eigenfrequency. In these regimes, there are difficulties with the description of relaxation processes without explicit consideration of environmental degrees of freedom. To correctly evaluate the relaxation rates, it is necessary to consider the interaction of the system with its environment taking into account the counter-rotating wave and diamagnetic terms. We develop a self-consistent theory for the calculation of the relaxation rates in the systems, in which the coupling strength is of the order of the system eigenfrequency. We demonstrate that the increase in the coupling strength can lead to a significant decrease in the relaxation rates. In particular, we show that, for frequency-independent density of states of the environment, the relaxation rates decrease exponentially with the increase in the coupling strength. This fact can be used to suppress losses by tuning the strength coupling and the environment states.