We study the quantum dynamics of a two-level system interacting with a quantized harmonic oscillator in the deep strong coupling regime (DSC) of the Jaynes-Cummings model, that is, when the coupling strength g is comparable or larger than the oscillator frequency ω (g/ω > ∼ 1). In this case, the rotating-wave approximation cannot be applied or treated perturbatively in general. We propose an intuitive and predictive physical frame to describe the DSC regime where photon number wavepackets bounce back and forth along parity chains of the Hilbert space, while producing collapse and revivals of the initial population. We exemplify our physical frame with numerical and analytical considerations in the qubit population, photon statistics, and Wigner phase space.The interaction between a two-level system and a harmonic oscillator is ubiquitous in different physical setups, ranging from quantum optics to condensed matter and applications to quantum information. Typically, due to the parameter accessibility of most experiments, the rotating-wave approximation (RWA) can be applied producing a solvable dynamics called the Jaynes-Cummings (JC) model [1]. In this case, Rabi oscillations inside the JC doublets or collapses and revivals of the system populations [2] are paradigmatic examples of the intuitive physics behind the JC dynamics. To achieve these and other phenomena in the lab, the strong coupling (SC) regime is required, that is, the qubit-oscillator coupling has to be comparable or larger than all decoherence rates. This model accurately describes the dynamics of cavity QED [3,4], trapped ion experiments [5], and several setups in mesoscopic physics, where the qubit-oscillator model is essential in modeling superconducting qubits [6] with either coplanar transmission lines [7][8][9][10] or nanomechanical resonators [11,12]. Nowadays, solid-state semiconductor [13] or superconductor systems [14][15][16][17][18][19][20] have allowed the advent of the ultrastrong coupling (USC) regime, where the coupling strength is comparable or larger than appreciable fractions of the mode frequency: g/ω > ∼ 0.1. In this regime, the RWA breaks down and the model becomes analytically unsolvable, although some limits can be explored [21][22][23][24][25]. Confident of the impressive fast development of current technology, one could explore further regimes where the rate between the coupling strength and oscillator frequency could reach g/ω > ∼ 1, here called deep SC (DSC) regime. This unusual regime, yet to be experimentally explored, is the focus of our current efforts. In this letter, we introduce a rigorous and intuitive description of the DSC regime of the JC model, providing an insightful picture where photon number wavepackets propagate coherently along two independent parity chains of states. In this way, the Hilbert space splits in two independent chains, exhibiting a comprehensible collapse-revival pattern of the system populations.We consider the Jaynes-Cummings Hamiltonian without the RWA, also called Rabi Hamiltonian, desc...

We propose a method to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. It supplements or substitutes the standard laser beam setups with auxiliary pulses that steer the system along the adiabatic path. Compared to other strategies, such as composite pulses or the original adiabatic techniques, it provides a fast and robust approach to population control.

We propose the quantum simulation of the quantum Rabi model in all parameter regimes by means of detuned bichromatic sideband excitations of a single trapped ion. We show that current setups can reproduce, in particular, the ultrastrong and deep strong coupling regimes of such a paradigmatic light-matter interaction. Furthermore, associated with these extreme dipolar regimes, we study the controlled generation and detection of their entangled ground states by means of adiabatic methods. Ion traps have arguably performed the first quantum simulation of the Jaynes-Cummings model, a restricted regime of the quantum Rabi model where the rotating-wave approximation holds. We show that one can go beyond and experimentally investigate the quantum simulation of coupling regimes of the quantum Rabi model that are difficult to achieve with natural dipolar interactions.

Abstract. Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a non-local potential. The second method, based on engineering an invariant of motion, only modifies the harmonic frequency in time, keeping the potential local at all times.

Type of publicationArticle (peer-reviewed) Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the "energy cost" of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption is possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and reused by perfect regenerative braking.