# How photons disappear?

A microwave photon that collides with a superconducting qubit can be split into several photons. This process is much more efficient than its optical analog in a crystal. We explained it by the quantum fluctuations in the electromagnetic environment of the qubit. Our theory has been used to interpret experiments on the lifetime of photons in superconducting circuits.

*Published on 20 May 2021*

Photons are grains of light that propagate in the vacuum with a well-defined energy. When they interact with matter, they can be transformed into photons of different energy. Thus, two photons can merge into a new photon whose energy is the sum of the energies of the initial photons. It is the non-linearity of the interaction between light and matter that makes this process possible. Conversely, can a photon spontaneously disappear, producing photons of smaller energy, when it travels through a crystal? While this process is classically forbidden, quantum physics allows it. It has even been used to produce pairs of entangled photons. However, this spontaneous fission of a visible or infrared photon is extremely inefficient: it only concerns a few photons per million.

*Figure: When a superconducting qubit (green) resonates with a microwave photon (purple) propagating in a transmission line (black), it can break it very efficiently into a quasi-resonant photon (blue) and several low energy photons (red).*

In arrays of Josephson junctions between superconducting islands, the oscillations of the superconducting phase difference propagate like optical photons, but at microwave frequencies. The advantage of these arrays is that one can introduce an extremely strong nonlinearity for these photons by reducing the size of the junctions. A small junction in series with a homogeneous chain of large junctions acts as a qubit coupled to a transmission line. The nonlinearity comes from the modulation of the qubit energy by the electric charge in its environment. This modulation is attributed to "quantum slips" of the phase difference at the small junction. Since the qubit energy depends on the charge, the quantum phase slips couple a quasi-resonant photon with the low-energy photons. With a researcher from Yale University, we have established that this coupling becomes particularly efficient to break a resonant photon into a quasi-resonant photon accompanied by many low-energy photons.

Photon lifetime has been measured in several superconducting circuits at the University of Maryland. Our theory, which attributes the disappearance of resonant photons to quantum phase slips, has allowed us to interpret the results for circuits characterized by a transmission line’s impedance greater than the resistance quantum. Outside this regime, other processes compete with quantum phase slips. To date, there is no theory to account for this. From this point of view, the experiments have realized a "quantum simulation" of a quantum impurity problem: the qubit coupled to its environment. Microwave photonics appears to be a promising field to study other complex quantum systems.