# Current Research

# Current Research

The current research activities of the Quantum Theory Group cover a wide range of activities, principally within the fields of quantum optics and quantum information, including quantum foundations. Our work is theoretical but we enjoy working closely with our experimental collaborators.

These few paragraphs are intended to convey only a flavour of our interests and highlight some of areas of expertise.

# Quantum information and quantum foundations

# Quantum information and quantum foundations

The development of quantum technologies presents both a chance to exploit to exotic quantum phenomena and also new questions for the foundations of quantum theory. We have a continuing interest and expertise in the forms of optimal measurements, including discrimination between a number of possible quantum states [1-3]. Such ideas are important, in particular, in quantum communications and we have an active interest in the study of quantum cryptography [4-5].

Pushing the limits of what is possible has encouraged investigation of rival formulations including the so-called PT-symmetric extension and also time-reversed or retrodictive quantum theory. We have shown that the former, when correctly formulated is fully compatible with conventional quantum theory and, contrary to some claims does not allow for violation of well-established bounds [6]. The retrodictive form embodies a synthesis of conventional predictive quantum theory with Bayes’ theorem and we have used this as the basis of a practical approach to image reconstruction [7,8].

# Light-matter interactions

# Light-matter interactions

The interaction between light and matter provides the most controllable arena for exploring and, indeed, exploiting quantum phenomena. The mechanical properties of light provide a wide variety of possibilities and we have explored the nature of the forces on atoms, on molecules (especially chiral molecules) [9-11] and on macroscopic bodies including those with a magnetic response [12,13]. Our work with atoms, in particular, highlighted the existence of a paradoxical vacuum friction force [14].

Light carries energy and momentum but also angular momentum and helicity. It propagates, moreover, in modes with a transverse spatial structure. We have explored the natures of these [15-21] and also the roles these play in light-matter interactions [22-26].

# References

# References

[1] *Difficulty of distinguishing product states*, Sarah Croke and Stephen M. Barnett; Physical Review A **95**, 012337 (2017).

[2] *Optimal sequential measurements for bipartite state discrimination*, Sarah Croke, Stephen M. Barnett and Graeme Weir; Physical Review A** 95**, 052308 (2017).

[3] *Optimal discrimination of single-qubit mixed states*, Graeme Weir, Stephen M. Barnett and Sarah Croke; Physical Review A **96**, 022312 (2017).

[4] *Cavity-enabled high-dimensional quantum key distribution*, Thomas Brougham and Stephen M. Barnett; Journal of Physics B: Atomic, Molecular and Optical Physics **47**, 155501 (2014).

[5] *The information of high-dimensional time-bin encoded photons*, Thomas Brougham, Christoph F. Wildfeuer, Stephen M. Barnett and Daniel J. Gauthier; European Physical Journal D **70**, 214 (2016).

[6] *PT-symmetric Hamiltonians and their application in quantum information*, Sarah Croke, Phys. Rev. A **91**, 052113 (2015)

[7] *Image retrodiction at low light levels*, Matthias Sonnleitner, John Jeffers and Stephen M. Barnett; Optica **2**, 950 (2015).

[8] *From retrodiction to Bayesian quantum imaging*, Fiona C. Speirits, Matthias Sonnleitner and Stephen M. Barnett; Journal of Optics **19**, 04401 (2017).

[9] *Disciminatory optical force for chiral molecules*, Robert P. Cameron, Stephen M. Barnett and Alison M. Yao; New Journal of Physics **16**, 013020 (2014).

[10] *Diffraction Gratings for Chiral Molecules and Their Applications*, Robert P. Cameron, Alison M. Yao and Stephen M. Barnett; The Journal of Physical Chemistry A **118**, 3472 (2014).

[11] *Matter-wave grating distinguishing conservative and dissipative interactions*, Robert P. Cameron, Jörg B. Götte, Stephen M. Barnett and J. P. Cotter; Physical Review A **94**, 013604 (2016).

[12] *Theory of radiation pressure on magneto-dielectric materials*, Stephen M. Barnett and Rodney Loudon; New Journal of Physics **17**, 063027 (2015).

[13] *Energy conservation and the constitutive relations in chiral and non-reciprocal media*, Stephen M. Barnett and Robert P. Cameron; Journal of Optics **18**, 015404 (2016).

[14] *Will a decaying atom feel a friction force?*, Matthias Sonnleitner, Nils Trautmann and Stephen M. Barnett; Physical Review Letters **118**, 053601 (2017).

[15] *Optical helicity of interfering waves*, Robert P. Cameron, Stephen M. Barnett and Alison M. Yao; Journal of Modern Optics **61**, 25 (2014).

[16] *Optical angular momentum in a rotating frame*. Fiona C. Speirits, Martin P. J. Lavery, Miles J. Padgett and Stephen M. Barnett; Optics Letters, **39**, 2994 (2014).

[17] *Generalized ray optics and orbital angular momentum carrying beams*, Václav Potoček and Stephen M. Barnett; New Journal of Physics **17**, 103034 (2015).

[18] *The azimuthal component of Poynting’s vector and the angular momentum of light*, Robert P. Cameron, Fiona C. Speirits, Claire Gilson, L. Allen and Stephen M. Barnett; Journal of Optics **17**, 125610 (2015).

[19] *Spatially structured photons that travel in free space slower than the speed of light*, Daniel Giovannini, Jacqueline Romero, Václav Potoček, Gergely Ferenczi, Fiona Speirits, Stephen M. Barnett, Daniele Faccio and Miles J. Padgett; Science **347**, 857 (2015).

[20] *On the natures of the spin and orbital parts of optical angular momentum*, Stephen M. Barnett, L. Allen, Robert P. Cameron, Claire R. Gilson, Miles J. Padgett, Fiona C. Speirits and Alison M. Yao; Journal of Optics **18**, 064004 (2016).

[21] *Chirality and the angular momentum of light*, Robert P. Cameron, Jörg B. Götte, Stephen M. Barnett and Alison M. Yao; Philosophical Transactions of the Royal Society A **375**, 20150433 (2017).

[22] *Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles*, D. B. Phillips, M. P. Lee, F. C. Speirits, S. M. Barnett, S. H. Simpson, M. P. J. Lavery, M. J. Padgett and G. M. Gibson; Physical Review A **90**, 011801(R) (2014).

[23] *Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body*, Martin P. J. Lavery, Stephen M. Barnett, Fiona C. Speirits and Miles J. Padgett; Optica **1**, 1 (2014).

[24] *Optical activity in the scattering of structured light*, Robert P. Cameron and Stephen M. Barnett; Physical Chemistry and Chemical Physics **16**, 25819 (2014).

[25] *Spatially Dependent Electromagnetically Induced Transparency*, N. Radwell, T. W. Clark, B. Piccirillo, S. M. Barnett and S. Franke-Arnold; Physical Review Letters **114**, 123603 (2015).

[26] *Chiral rotational spectroscopy*, Robert P. Cameron, Jörg B. Götte and Stephen M. Barnett; Physical Review A **94**, 032505 (2016).