Fock state | EPFL Graph Search

In quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an important role in the second quantization formulation of quantum mechanics. The particle representation was first treated in detail by Paul Dirac for bosons and by Pascual Jordan and Eugene Wigner for fermions. The Fock states of bosons and fermions obey useful relations with respect to the Fock space creation and annihilation operators. Definition One specifies a multiparticle state of N non-interacting identical particles by writing the state as a sum of tensor products of N one-particle states. Additionally, depending on the integrality of the particles' spin, the tensor products must be alternating (anti-symmetric) or symmetric products of the underlying one-particle Hilbert space. Specifically:

Fermions, having half-integer

Non-classical photon-phonon correlations at room temperature

Santiago Tarrago Velez

With the development of quantum optics, photon correlations acquired a prominent role as a tool to test our understanding of physics, and played a key role in verifying the validity of quantum mechanics. The spatial and temporal correlations in a light field also reveal information about its origin, and allow us to probe the nature of the physical systems interacting with it. Additionally, with the advent of quantum technologies, they have acquired technological relevance, as they are expected to play an important role in quantum communication and quantum information processing.This thesis develops techniques that combine spontaneous Raman scattering with Time Correlated Single Photon Counting, and uses them to study the quantum mechanical nature of high frequency vibrations in crystals and molecules. We demonstrate photon bunching in the Stokes and anti-Stokes fields scattered from two ultrafast laser pulses, and use their cross-correlation to measure the 3.9 ps decay time of the optical phonon in diamond. We then employ this method to measure molecular vibrations in CS2, where we are able to excite the respective vibrational modes of the two isotopic species present in the sample in a coherent superposition, and observe quantum beating between the two signals. Stokes scattering, when combined with a projective measurement, leads to a well defined quantum state. We demonstrate this by measuring the second order correlation function of the anti-Stokes field conditional on detecting one or more photons in the Stokes field, which allows us to observe a phonon modeâs transition form a thermal state into the first excited Fock state, and measure its decay over the characteristic phonon lifetime. Finally, we use this technique to prepare a highly entangled photon-phonon state, which violates a Bell-type inequality. We measure S = 2.360 Â± 0.025, violating the CHSH inequality, compatible with the non-locality of the state.The techniques we developed open the door to the study of a broad range of physical systems, where spectroscopic information is obtained with the preparation of specific quantum states. They also hold potential for future technological use, and promote vibrational Raman scattering to a resource in nonlinear quantum optics -- where it used to be considered as a source of noise instead.

EPFL2021

Two-Color Pump-Probe Measurement of Photonic Quantum Correlations Mediated by a Single Phonon

Mitchell David Anderson, Hugo Pierre Alexandre Flayac, Christophe Marcel Georges Galland, Vincenzo Savona, Kilian Robert Seibold, Santiago Tarrago Velez

We propose and demonstrate a versatile technique to measure the lifetime of the one-phonon Fock state using two-color pump-probe Raman scattering and spectrally resolved, time-correlated photon counting. Following pulsed laser excitation, the n = 1 phonon Fock state is probabilistically prepared by projective measurement of a single Stokes photon. The detection of an anti-Stokes photon generated by a second, time-delayed laser pulse probes the phonon population with subpicosecond time resolution. We observe strongly nonclassical Stokes-anti-Stokes correlations, whose decay maps the single phonon dynamics. Our scheme can be applied to any Raman-active vibrational mode. It can be modified to measure the lifetime of n >= 1 Fock states or the phonon quantum coherences through the preparation and detection of two-mode entangled vibrational states.

2018

Preparation and Decay of a Single Quantum of Vibration at Ambient Conditions

Mitchell David Anderson, Christophe Marcel Georges Galland, Nils Kipfer, Kilian Robert Seibold, Vivishek Sudhir

A single quantum of excitation of a mechanical oscillator is a textbook example of the principles of quantum physics. But mechanical oscillators, despite their pervasive presence in nature and modem technology, do not genetically exist in an excited Fock state. In the past few years, careful isolation of gigahertz-frequency nanoscale oscillators has allowed experimenters to prepare such states at millikelvin temperatures. These developments illustrate the tension between the basic predictions of quantum mechanics-which should apply to all mechanical oscillators even at ambient conditions-and the extreme conditions required to observe those predictions. We resolve the tension by creating a single Fock state of a 40-THz vibrational mode in a crystal at room temperature and atmospheric pressure. After exciting a bulk diamond with a femtosecond laser pulse and detecting a Stokes-shifted photon, the Raman-active vibrational mode is prepared in the Fock state vertical bar 1 > with 98.5% probability. The vibrational state is then mapped onto the anti-Stokes sideband of a subsequent pulse, which when subjected to a Hanbury Brown-Twiss intensity correlation measurement reveals the sub-Poisson number statistics of the vibrational mode. By controlling the delay between the two pulses, we are able to witness the decay of the vibrational Fock state over its 3.9-ps lifetime at ambient conditions. Our technique is agnostic to specific selection rules, and should thus be applicable to any Raman-active medium, opening a new general approach to the experimental study of quantum effects related to vibrational degrees of freedom in molecules and solid-state systems.

2019

Non-classical photon-phonon correlations at room temperature

Santiago Tarrago Velez

EPFL2021