Generation and detection of squeezed phonons in lattice dynamics by ultrafast optical excitations

We propose a fully quantum treatment for pump and probe experiments applied to the study of phonon excitations in solids. To describe the interaction between photons and phonons, a single effective hamiltonian is used that is able to model both the excitation induced by pump laser pulses and the subsequent measuring process through probe pulses. As the photoexcited phonons interact with their surroundings, mainly electrons and impurities in the target material, they cannot be considered isolated: their dynamics needs to be described by a master equation that takes into account the dissipative and noisy effects due to the presence of the environment. In this formalism, the quantum dynamics of pump excited phonons can be analyzed through suitable probe photon observables; in particular, a clear signature of squeezed phonons can be obtained by looking simultaneously at the behavior of the scattered probe mean photon number and its variance

Numerical modeling of the multi-stage Stern\unicode{x2013}Gerlach experiment by Frisch and Segr\`e using co-quantum dynamics via the Bloch equation

We numerically study the spin flip in the Frisch\unicode{x2013}Segr\`e experiment, the first multi-stage Stern\unicode{x2013}Gerlach experiment, within the context of the novel co-quantum dynamics theory. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. Our results show that, without using any fitting parameters, the co-quantum dynamics closely reproduces the experimental observation reported by Frisch and Segr\`e in 1933, which has so far lacked theoretical predictions.Comment: 9 pages, 6 figure

Numerical modeling of the multi-stage Stern\unicode{x2013}Gerlach experiment by Frisch and Segr\`e using co-quantum dynamics via the Schr\"odinger equation

We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern\unicode{x2013}Gerlach (SG) experiment conducted by R. Frisch and E. Segr\`e. This experiment consists of two Stern\unicode{x2013}Gerlach apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch\unicode{x2013}Segr\`e experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schr\"odinger equation. Our simulation outcome agrees with the Frisch\unicode{x2013}Segr\`e experimental observation and supports CQD as a potential model for electron spin evolution and collapse.Comment: 13 pages, 3 figure

Quantum mechanical modeling of the multi-stage Stern\unicode{x2013}Gerlach experiment by Frisch and Segr\`e using the von Neumann equation

The multi-stage Stern\unicode{x2013}Gerlach experiment conducted by Frisch and Segr\`e has been modeled analytically using quantum mechanics by Majorana and revised by Rabi by including the hyperfine interaction. However, the theoretical predictions do not match the experimental observation well. Here, we numerically solve the standard quantum mechanical model, via the von Neumann equation, that includes the hyperfine interaction for the time evolution of the spin. The outcome is compared with the experimental observation and the predictions by Majorana, Rabi, and an alternative model called co-quantum dynamics. Thus far, the coefficients of determination from the standard quantum mechanical model, which does not use free parameters, are still below zero. Non-standard variants that improve the match are explored for discussion.Comment: 8 pages, 5 figure

Photon number statistics uncover the fluctuations in non-equilibrium lattice dynamics

Fluctuations of the atomic positions are at the core of a large class of unusual material properties ranging from quantum para-electricity to high temperature superconductivity. Their measurement in solids is the subject of an intense scientific debate focused on seeking a methodology capable of establishing a direct link between the variance of the atomic displacements and experimentally measurable observables. Here we address this issue by means of non-equilibrium optical experiments performed in shot-noise limited regime. The variance of the time dependent atomic positions and momenta is directly mapped into the quantum fluctuations of the photon number of the scattered probing light. A fully quantum description of the non-linear interaction between photonic and phononic fields is benchmarked by unveiling the squeezing of thermal phonons in $\alpha$-quartz.Comment: 7 pages (main text), 5 figures, 11 pages (supplementary information

Pulsed homodyne Gaussian quantum tomography with low detection efficiency

Pulsed homodyne quantum tomography usually requires a high detection efficiency limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency ($<50\%$) does not prevent the tomographic reconstruction of quantum states of light, specifically, of Gaussian type. This result is obtained by applying the so-called "minimax" adaptive reconstruction of the Wigner function to pulsed homodyne detection. In particular, we prove, by both numerical and real experiments, that an effective discrimination of different Gaussian quantum states can be achieved. Our finding paves the way to a more extensive use of quantum tomographic methods, even in physical situations in which high detection efficiency is unattainable

Generazione e rilevazione di fononi "squeezed" in esperimenti di "pump and probe": trattazione quantistica

2013/2014Femtosecond pump and probe techniques are standard experimental methodologies used for studying ultrafast dynamics in solids, in particular phonon oscillations in target materials. So far, only semiclassical methods have been employed in order to theoretically interpret the experimental data. In contrast, a fully quantum treatment will be presented here taking into account the quantum features of the generation mechanism of excited phonons by pump laser pulses, and of the process of accessing their behaviour by probe laser pulses. A single effective Hamiltonian will be used to model the interaction between photons and phonons both for the pumping and probing processes. In addition, as they interact with their environment, mainly electrons in the target, the excited phonons cannot be considered an isolated system. Their dynamics is then that typical of open quantum systems and generated by a master equation of Lindblad form, that takes into account the dissipative and noisy effects due to the environment.In this formalism, phonon oscillations can be analysed through suitable probe photon observables. Specifically, unlike in the existing literature, we will not focus only upon the scattered probe pulse intensity, namely on the probe photon number, but also on the number variance. Through the latter some quantum features of the phonon state can be accessed; in particular, specific signals of the presence of squeezed phonons can thus be identified.Le tecniche di "pump and probe" impulsato sono metodologie sperimentali standard usate nello studio delle dinamiche ultraveloci nei solidi, in particolare delle oscillazioni di fononi. Usualmente l'interpretazione teorica dei dati sperimentali si basa su approssimazioni semiclassiche. Una descrizione completamente quantistica e` invece sviluppata nella presente trattazione: e` basata sull'introduzione di un'unica hamiltoniana di interazione tra fotoni e fononi, capace di descrivere in modo effettivo sia il processo di eccitazione che di rivelazione dei fononi. In generale, tali fononi non possono essere considerati come isolati, ma costituiscono un sistema quantistico aperto, cioe` in interazione debole con l'ambiente esterno, formato principalmente da elettroni e dagli altri costituenti del materiale in studio. La loro dinamica deve percio` venir descritta tramite una equazione master, che tenga conto di effetti di rumore e dissipazione. In questo formalismo, le proprieta` dei fononi eccitati dagli impulsi laser di "pump" possono essere analizzate attraverso lo studio di opportune osservabili caratterizzanti i fotoni di "probe". Piu` specificatamente, si e` analizzato il comportamento non solo dell'intensita` media della luce di "probe" riflessa, cioe` del numero medio di fotoni, ma anche della relativa varianza. In questo modo, si possono evidenziare alcune caratteristiche quantistiche dei fononi: in particolare, sono stati individuati segnali specifici della presenza di fononi "squeezed"XXVII Ciclo198

Quantum interferences reconstruction with low homodyne detection efficiency

Optical homodyne tomography consists in reconstructing the quantum state of an optical field from repeated measurements of its amplitude at different field phases (homodyne data). The experimental noise, which unavoidably affects the homodyne data, leads to a detection efficiency eta 0.5) below which quantum features, like quantum interferences, cannot be retrieved. Here, by numerical experiments, we demonstrate that quantum interferences can be effectively reconstructed also for low homodyne detection efficiency. In particular, we address the challenging case of a Schrodinger cat state and test the minimax and adaptive Wigner function reconstruction technique by processing homodyne data distributed according to the chosen state but with an efficiency. < 0.5. By numerically reproducing the Schrodinger's cat interference pattern, we give evidence that quantum state reconstruction is actually possible in these conditions, and provide a guideline for handling optical tomography based on homodyne data collected by low efficiency detectors