What is a Fock State ?
A Fock state is a quantum state with a well-defined number of identical particles. It is also called a number state. The particles in a Fock state are identical, in the sense that they share the same properties, and are indistinguishable.
In quantum optics, an example of a Fock state of light is a number \(n\) of identical photons traveling in the same spatial mode; such state is denoted \( ket{0}\) ,\( ket{1} \) \( ket{2}\) are examples of Fock states on one mode with respectiviely 0 (vacuum state), 1 and 2 particles. Formally, for m modes we can write a Fock state as
$$ \ket{n_1, n_2, …, n_m} $$
Fock states are also called occupancy number basis states and are used to describe the statistics of particles such as fermions or bosons. These statistics are defined by the behaviour of the fermionic or bosonic creation and annihilation operators. In the case of fermions, the Pauli exclusion principle imposes \( n_i=0,1 \). On the opposite, multiple bosons can occupy the same mode, \( n_i=0,1,2,…\).
In quantum computing, Fock states can be used to encode qubits using the dual-rail encoding scheme, or in the task of boson sampling.
Frequently asked questions
- What is the difference between a Fock state and a coherent state?
A coherent state is a parametrized superposition of Fock states with all particle numbers. It can be expressed in the Fock basis as
$$ \ket{\alpha} = e^{-|\alpha|^2/2}\frac{\alpha^n}{\sqrt{n!}}\ket{n} $$
Coherent states are classical states of light that can be obtained typically by a laser source. In contrary, Fock states are highly non-classical.
- Can we experimentally create Fock states?
Yes, Fock states can be experimentally realized via single photon sources. They can also be engineered in different quantum computing technologies such as cavity QED, superconducting qubits or trapped ions.