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arXiv:2407.04389

Unitary death of Schrödinger's cat

Pavel Stránský, Pavel Cejnar, Radim Filip

Published Jul 5, 2024• 0 citations
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Abstract

We analyze dynamics of the Rabi model describing interactions of a qubit with a single soft-mode oscillator. We show that the model with a slightly violated parity generates symmetric Schr{ö}dinger cat states of the oscillator, which suddenly perish in a spontaneous unitary process similar to the measurement-induced wave-function collapse. The effect is sufficiently robust to be tested experimentally, e.g., with trapped ions, macroscopic mechanical oscillators or superconducting circuits.

DOI
10.48550/arxiv.2407.04389

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We analyze dynamics of the Rabi model describing interactions of a qubit with a single soft-mode oscillator. We show that the model with a slightly violated parity generates symmetric Schr{ö}dinger cat states of the oscillator, which suddenly perish in a spontaneous unitary process similar to the measurement-induced wave-function collapse. The effect is sufficiently robust to be tested experimentally, e.g., with trapped ions, macroscopic mechanical oscillators or superconducting circuits.
Almost a century after the development of quantum mechanics, we still do not have a consensus on the process of collapse of wavefunctions. Some theories require the intervention of a conscious observer while some see it as a stochastic process, and most theories violate energy conservation. In this paper we hypothesise that the collapse of wavefunctions can be caused by interactions with other objects (macroscopic or microscopic) and energy is conserved in that process. To test various hypotheses regarding collapse of wavefunctions, we propose a model system which is the quantum analogue of a classical soft-impact oscillator. We propose some alternative postulates regarding the conditions for and the result of a collapse, and obtain the implication of each on the behavior of observable quantities, which can possibly be experimentally tested.
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We study the dynamics of the Jaynes-Cummings Model for an array of NqN_qNq​ two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). For an initial cavity coherent state ∣α>| α>∣α> and the qubit system in a specified `basin of attraction' in its Hilbert space, we demonstrate the oscillation of a superposition of two macroscopic quantum states between the qubit system and the field mode. From the perspective of either the qubit or the field system, there is collapse and revival of a `Schrödinger Cat' state.
Quantum mechanics is grounded on the superposition principle, which is the source both of its tremendous success and technological power, as well as of the problems in understanding it. The reason why superpositions do not propagate from the microscopic to the macroscopic world are subject to debate. Spontaneous wave function collapse models have been formulated to take into account a progressive breakdown of quantum superpositions when systems are large enough; they do so by modifying the Schrödinger dynamics, and therefore they are empirically testable. Deviations are tiny, and require precision measurements. I will review collapse models, and present the most recent experimental tests.
Although quantum mechanics is a mature theory, fundamental problems discussed during its time of foundation have remained with us to this day. These problems are centered on the problematic relation between the quantum and classical worlds. The most famous element is the measurement problem, i.e., the measurement of a quantum system by a classical apparatus, and the concomitant phenomena of wave packet reduction, the appearance of probability, and the problems related to Schrödinger cat states. A fundamental question in this context is whether quantum mechanics can bootstrap itself to the classical world: is quantum mechanics self-consistent, such that the measurement process can be understood within quantum mechanics itself, or does this process require additional elements from the realm outside of traditional quantum mechanics? Here, we point to a problematic aspect in the traditional Schrödinger cat argument which can be overcome through its extension with a proper macroscopic preparation device; the deliberate creation of a cat state and its identification then turns into a non-trivial problem requiring the determination of the evolution of a quantum system entangled with a macroscopic reservoir. We describe a new type of wave-function correlator testing for the appearance of Schrödinger cat states and discuss its implications for theories deriving the wave function collapse from a unitary evolution.