Finite-time quantum-to-classical transition for a Schrödinger-cat state

Abstract

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schrödinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schrödinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a sudden death. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.

Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment

“…As we will show in the following sections, the memory effects associated with the interaction with a classical OU field allows the initial state to preserve its nonclassicality for times longer than those achieved with a Markovian environment. As we will see, the smaller γ is, the longer the survival time of quantumness at fixed values of the detuning δ. Conversely, for γ 1, the survival time of the Schrödinger-cat state approaches the Markovian values [25]. Indeed, for γ 1 the autocorrelation function in Eq.…”

“…As we mentioned earlier, we have chosen |α| = √ 2 for the Schrödinger-cat state. In turn, this choice maximizes the effectiveness of the Klyshko criterion, i.e., is the value corresponding to the longest survival time by the Klyshko criterion [25].…”

“…In this context, a thoroughly studied quantum system is the single-mode quantum harmonic oscillator interacting with a bosonic bath of oscillators. For such an open system, the decoherence time, ruling the transition from the quantum to the classical regime, may be identified by different nonclassicality criteria, which have been widely investigated [11][12][13][14][15][16][17][18][19][20][21][22][23][24] and compared [25]. Extensions to multimode systems [26][27][28][29] have been analyzed and the decoherence process has been addressed extensively [30,31].…”

Detecting quantum non-Gaussianity of noisy Schrödinger cat states

“…> 0.5 such that no negativity of the Wigner function can be observed [15]. In particular we will determine the maximum values for which we observe a violation…”

Generating the Schrödinger cat state in a nanomechanical resonator coupled to a charge qubit

“…Generating large quantum superposition of the macroscopic objects is an essential task in the field of the macroscopic quantum mechanics [3][4][5][6], which provides a good platform to understand the mechanism of decoherence in macroscopic objects [7,8], to check the scope of application of quantum theory [9] and to observe the transition between quantum and classical physics [10]. To this end, the large quantum superposition, like the Schrödinger cat state (simply called 'cat state' in the following), has been realized in various systems, such as trapped ions [11], photons [12], superconducting qubits [13], macroscopic current [14], and NAMR [15].…”