Supervisors: 
Prof Terry Rudolph (Imperial College London)
Dr. David Jennings (Imperial College London)
Dr. Sean Barrett (Imperial College London)

Continuous Matrix Product States and Quantum Optics

One of the most important developments in quantum information in recent years is the discovery of new methods for understanding quantum many body systems. An important feature of these techniques are the representations of the ground states of  many body systems, such as Matrix Product States (MPS), which can describe highly entangled states with a number of parameters that grows only polynomially with the number of particles in the system. A very recent development has been to extend these techniques to describe the low energy states of quantum field theories (QFTs) [1] that involve infinite dimensional objects that are described in a continuous region of space. The resulting many-body variational wavefunctions (for 1-D field theories) are known as Continuous Matrix Product States (CMPS).

Recently, an interesting connection was made between CMPS's, and the states that are output from an optical cavity (see [2]), if the internal dynamics of the cavity is carefully controlled. Optical cavities, containing atoms, whose dynamics are controlled, have long been objects of study in the quantum optics community.

Moreover, the input-output formalism, for describing the quantum state of the electromagnetic field leaking out of an optical cavity (see e.g. [3]) is the natural tool to study the cavities as it bears similarities with the equations describing a CMPS. Part of this project will be devoted to developing this connection further.

References

[1] F. Verstraete, J.I. Cirac, Phys.Rev.Lett.104:190405,2010; T. J. Osborne, J. Eisert, F. Verstraete Phys. Rev. Lett. 105, 260401 (2010).

[2] T. J. Osborne, J. Eisert, F. Verstraete Phys. Rev. Lett. 105, 260401 (2010).

[3] `Quantum Noise,' C. Gardiner and P. Zoller, Springer, (2000)