**Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?**

Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur GraphSearch.

Concept# Fock state

Résumé

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.
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 spin and obeying the Pauli exclusion principle, correspond to antisymmetric tensor products.
Bosons, possessing integer spin (and not governed by the exclusion principle) correspond to symmetric tensor products.
If the number of particles is variable, one constructs the Fock space as the direct sum of the tensor product Hilbert spaces for each particle number. In the Fock space, it is possible to specify the same state in a new notation, the occupancy number notation, by specifying the number of particles in each possible one-particle state.
Let be an orthonormal basis of states in the underlying one-particle Hilbert space. This induces a corresponding basis of the Fock space called the "occupancy number basis". A quantum state in the Fock space is called a Fock state if it is an element of the occupancy number basis.
A Fock state satisfies an important criterion: for each i, the state is an eigenstate of the particle number operator corresponding to the i-th elementary state ki. The corresponding eigenvalue gives the number of particles in the state.

Source officielle

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés (20)

Personnes associées (1)

Publications associées (3)

Cours associés (9)

Unités associées (1)

Creation and annihilation operators

Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted ) lowers the number of particles in a given state by one. A creation operator (usually denoted ) increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator.

Fock state

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.

Miroir semi-réfléchissant

Un miroir semi-réfléchissant est un type de miroir dont la particularité est de ne réfléchir qu'une partie de la lumière qu'il reçoit, et de laisser passer l'autre partie (indépendamment de sa couleur, avec la technologie actuelle). En d'autres termes, il sépare un rayon incident en deux flux lumineux, l'un réfléchi, l'autre réfracté (la partie diffusée, de plus faible quantité, étant négligeable, de même que la partie absorbée, transformée en chaleur).

Séances de cours associées (64)

PHYS-453: Quantum electrodynamics and quantum optics

This course on one hand develops the quantum theory of electromagnetic radiation from the principles of quantum electrodynamics. It will cover basis historic developments (coherent states, squeezed st

CH-244: Quantum chemistry

Introduction to Quantum Mechanics with examples related to chemistry

PHYS-431: Quantum field theory I

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.

Quarks et Leptons: Spin-1/2 et Dirac Notation

Présente les quarks et les leptons, discutant de leur spin, charge et notation.

Mécanique quantique : deuxième quantificationPHYS-314: Quantum physics II

Explore la deuxième quantification en mécanique quantique, mettant l'accent sur les opérateurs de création et d'annihilation dans les espaces Hilbert et Fock.

Quantum Mécanique: Hilbert Espace et opérateursCH-244: Quantum chemistry

Couvre les concepts fondamentaux de la mécanique quantique, en mettant l'accent sur les espaces et les opérateurs Hilbert.

Vincenzo Savona, Christophe Marcel Georges Galland, Hugo Pierre Alexandre Flayac, Mitchell David Anderson, 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, , , ,

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.

2019With 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.