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arXiv:1903.05378 · Physical Review Letters

Experimental Investigation of Quantum Decay at Short, Intermediate, and Long Times via Integrated Photonics

Andrea Crespi, Francesco Vincenzo Pepe, Paolo Facchi A, Fabio Sciarrino, Paolo Mataloni, Hiromichi Nakazato, Saverio Pascazio, Roberto Osellame

Published Apr 3, 2019• 56 citations
arXivHTMLPDF

Abstract

The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: Indeed, the decay is initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to distinct quantum states of the photon, and the temporal evolution of the quantum system is mapped into the spatial propagation coordinate. By injecting coherent light states in the fabricated photonic structures and by measuring a small scattered fraction of such light with an unprecedented dynamic range, we are able to experimentally observe not only the exponential decay regime, but also the quadratic Zeno region and the power-law decay at long evolution times.

DOI
10.1103/physrevlett.122.130401

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The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: Indeed, the decay is initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to distinct quantum states of the photon, and the temporal evolution of the quantum system is mapped into the spatial propagation coordinate. By injecting coherent light states in the fabricated photonic structures and by measuring a small scattered fraction of such light with an unprecedented dynamic range, we are able to experimentally observe not only the exponential decay regime, but also the quadratic Zeno region and the power-law decay at long evolution times.
Whereas classical physics generally predicts an exponential trend for the temporal decay of an unstable state, quantum mechanics provides a rather different description. The decay is initially quadratic, while at very large times it follows a power-law. Actually, the latter regime has never been observed experimentally. Here we employ arrays of femtosecond-laser-written optical waveguides to optically realize quantum systems where a discrete state is coupled to and can decay into a continuum. The transverse optical modes represent distinct quantum states of the photon and the temporal evolution of the system is mapped into the longitudinal propagation coordinate. By injecting laser light in the fabricated structures, and by imaging with high dynamic range the scattered light from above, we are able to observe experimentally different decay regimes, including the power-law tail. This process can be viewed as the quantum simulation of a quantum decay phenomenon.
We investigate the spontaneous emission of a two-level system coupled to a photonic waveguide, showing that dynamical dephasing in the photon modes profoundly alters the decay law. In the absence of dephasing, the emitter displays conventional exponential decay followed by a long-time power-law tail -- observable only at extremely low survival probabilities. Strikingly, when dephasing is introduced, a robust power-law decay emerges already at short times, driven by photon diffusion in the dynamically disordered environment rather than spectral edge effects. These results reveal a novel, decoherence-induced mechanism for non-exponential spontaneous emission in waveguide QED platforms.
Frequent observations to a quantum system modify its coherent evolution through the Zeno effect and Zeno dynamics. Generally, the measurement process destroys the evolution environment of the monitored system, making repeated observations remain a challenge. Here, using the quantum analogy experiments, we realize and engineer the Zeno effect and Zeno dynamics in optical waveguide arrays, where the optical modes correspond to distinct quantum states, and the temporal evolution is mapped into the spatial propagation. We propose a new, extensible experimental strategy for realizing an optical analog of stroboscopic measurements, which are performed by the build-in, on-demand segmented waveguide portions. The weak-to-strong stroboscopic measurements are realized, where the monitored system undergoes a transition from free evolution to optical Zeno freezing. Setting the measurements in the strong regime, the optical Zeno effect and optical Zeno dynamics are successfully generated, and their relationship is demonstrated in optics. We then propose a novel quantum Zeno slicing approach, which allows us to dynamically engineer the Hilbert space of the monitored system. This generic approach is verified by generating a series of Zeno subspaces with different measurement projectors, based on the quantum-optical analogy. The complexity of light dynamics is largely increased, providing full control of the propagation via steering Zeno dynamics. Our results pave the way for manipulation of quantum states by harnessing Zeno dynamics in integrated photonics.
ABSTRACT We investigate the spontaneous emission of a two‐level system coupled to a photonic waveguide, showing that dynamical dephasing in the photon modes profoundly alters the decay law. In the absence of dephasing, the emitter displays conventional exponential decay followed by a long‐time power‐law tail – observable only at extremely low survival probabilities. Strikingly, when dephasing is introduced, a robust power‐law decay emerges already at short times, driven by photon diffusion in the dynamically disordered environment rather than spectral edge effects. These results reveal a novel, decoherence‐induced mechanism for non‐exponential spontaneous emission in waveguide QED platforms.
We propose a methodical approach to controlling and enhancing deviations from exponential decay in quantum and optical systems by exploiting recent progress surrounding another subtle effect: the bound states in the continuum, which have been observed in optical waveguide array experiments within this past decade. Specifically, we show that by populating an initial state orthogonal to that of the bound state in the continuum, it is possible to engineer system parameters for which the usual exponential decay process is suppressed in favor of inverse power law dynamics and coherent effects that typically would be extremely difficult to detect in experiment. We demonstrate our method using a model based on an optical waveguide array experiment and further show that the method is robust even in the face of significant detuning from the precise location of the bound state in the continuum.