Focking lasers, how do they work?

Fock lasers based on deep-strong coupling of light and matter

This summary is a little late because the preprint was posted when I was travelling last year.

This paper proposes a new kind of quantum light source using hybrid light-matter systems in the deep strong coupling regime. This is the regime in which the photonic mode with frequency ω (say, a microwave cavity) and a two-level system with transition frequency ω0 (such as a superconducting qubit) are coupled with a strength g >> ω, ω0. This hybrid system can act as a cavity with an effective nonlinearity of extremely high order, which gives rise to an N-photon blockade: the first N states can be populated, but the (N+1)th state cannot. When this hybrid system is coupled to an external pump it relaxes to a steady state in which the photon number distribution is strongly peaked at a Fock state with N = g^2 photons.

How does it work? The key is the spectrum of the hybrid system in the deep strong coupling regime. The low energy spectrum looks just like an ordinary quantum harmonic oscillator, with a uniform spacing ω between adjacent energy levels. But the eigenstates look very different, thanks to the photon-qubit coupling.

The ground state is twofold degenerate: the photonic mode is in a (Gaussian) coherent state displaced from the origin by +g (or -g), while the qubit's spin points in the -x (or +x) direction. Since g is large, these two states have a negligible overlap with each other; they are essentially independent.

 

 Two degenerate ladders of excited states are obtained by adding photons to each ground state. Each photon added increases the energy by ω (hence, the linear spectrum). The photonic wavefunction broadens and becomes more strongly oscillatory, just like excited states of the quantum harmonic oscillator. But each wavefunction's centre of mass is displaced by +g (or -g).

When the photon number reaches the critical value of N = g^2, the photonic parts of the two wavefunctions start to overlap and can therefore interfere. This means that the two ladders can no longer be treated independently; they become coupled. Interference between the -x and +x spin states of the qubit generates a nonzero z component of the spin. This gives an additional energy shift ω0 𝜎z (due to the qubit part of the Hamiltonian) that destroys the uniform level spacing. Because the large n harmonic oscillator wavefunctions oscillate rapidly, this energy shift is highly sensitive to n, making the spectrum nonlinear for n > g^2. Thus, only N quanta with energy ω can be resonantly coupled to the system before it tunes itself out of resonance. This is the mechanism behind the N-photon blockade.

These plots are based on g = 5. State-of-the-art experiments can reached g=2. Hopefully further improvements in superconducting quantum circuits will allow us to push g to even higher values.