I recognised that the amplification of squeezed light with linear optical amplifiers could be improved using phase sensitive (squeezed) amplifiers. I also investigated the phase properties of nonclassical states of light, non-linear materials (Kerr media) and linear amplifiers in terms of the newly-introduced Pegg-Barnett phase formalism.
I have examined fundamental questions concerning the definition of quantum optical phase including the consistency of various phase formalisms and the treatment of the Pegg-Barnett formalism in the infinite dimensional limit. This work helped resolve some confusion in the literature and the publications. I developed the minimum uncertainty states and the so-called intelligent states associated with the photon number and phase operators. This had never been done before, and the work remains a cornerstone for the theory of quantum phase. I introduced a new phase formalism based on a Hilbert space which includes vectors representing states of infinite photon number. This work led to the definition of a new Wigner function for the photon number and phase observables. The new Wigner function is unique in the sense that it is the only quasiprobability distribution introduced to date for which the marginal distributions are the photon number and the phase probability distributions. It gives new insights into the number-phase properties of non-classical states. My work on the theory of the quantum phase operator from its beginning in 1989 lead to my co-authoring a book in 2007 that reviews the research field.
I developed a technique for probing the long-range spatial order in 1 dimensional optical lattices in laser cooled gasses (which was previously thought impossible). I gave the theoretical support to a collaboration which investigated electromagnetically induced transparency (EIT) experimentally. Our collaboration was the first to demonstrate EIT in laser cooled gases, transient EIT and EIT with weak fields. We also demonstrated EIT and optical gain in novel transition configurations. I developed a three-dimensional model of EIT and related effects using stochastic wavefunctions. This model gives a clear pictorial representation of the underlying physics of ``counter-intuitive pulse sequences'' in population transfer and EIT.
I showed how the phase of a Bose-Einstein condensate could be interpreted in terms of robust states. I showed that robust states play an important role in the emergence of preferred states in open quantum systems. I applied robust states analysis to the state of an atom laser showing the effect of the nonlinearities in the atomic cloud.
I have proven the no-go theorem for quantum remote control, showing it is not possible to arbitrarily control a quantum system remotely. This theorem is on par with the no-cloning theorem of Wootters and Zurek. I then showed a restricted class of operation could be implemented remotely. The latter work has been confirmed experimentally by Xiang et al. Phys.Rev.A 71, 044304 (2005).
I designed a linear-optical experiment to demonstrate the principle of quantum coding (quantum data compression). This principle lies at the foundation of quantum information and underpins the concept of the qubit as a unit of quantum information. The experiment was performed by Sasaki's group at the Communications Research Laboratory (CRL), Tokyo. We have been granted patents in the UK, Japan and the USA covering the techniques involved. I am a named inventor on the patents.
My work on entanglement in the presence of superselection rules, the quantification of the associated reference frames is central to understanding entanglement and other nonlocal resources. A key element of this is my definition of quantum asymmetry.
One of the basic elements of quantum theory that sets it apart from classical theory is the complementarity principle which restricts the information about particular observables of a quantum system. I have found that this principle can be framed in terms of the dichotomy between the symmetry and asymmetry of a system with respect to a given symmetry group.
I have challenged the accepted wisdom that the erasure of information incurs an energy cost according to Landauer's erasure principle. I have shown that by replacing the conventional thermal reservoir with a spin reservoir the cost of erasure can, in principle, be in terms of spin angular momentum and not energy. The significance of this result for the foundations of Thermodynamics cannot be overstated. By resolving Maxwell's demon paradox, Landauer's erasure restores the validity Second Law; as such, it is regarded as being equivalent to the Second Law. The new erasure mechanism implies a new statement of the Second Law is needed. Indeed, erasing the memory of the demon using a spin reservoir means all the heat in a thermal reservoir can be extracted in the form of mechanical work, in contradistinction to historical statements of the Second Law.
Processes that violate time reversal invariance (T), such as neutral K meson decay, depend on the direction of time. Although T violation has been recognised as important in terms of the nature of time, no one has previously been able to find the role it plays. I have recently solved this problem by showing that T violation processes underlie a mechanism that is responsible for the unidirectionality of time (i.e. for a specific direction of time). This groundbreaking research introduces a quantum theory of time that overhauls our understanding the physical nature of time.