I have started a new website that I will use instead.

See http://www-staff.lboro.ac.uk/~phmje/MJE_Home/Main.html

It seems that blogging does not suit me.

I have started a new website that I will use instead.

See http://www-staff.lboro.ac.uk/~phmje/MJE_Home/Main.html

We have just had the following article published on line:

M.J. Everitt, W.J. Munro and T.P. Spiller

Below is a brief summary that is supposed to be accessible to a general audience.

In this work we show that we can take a photonic device and use it either as a quantum resources or a classical control field simply by changing its environment. Quantum communication technologies are a reality today, and the first steps are now being taken towards other new technologies that sense, process and store information using quantum resources. These new technologies get their power by leveraging properties, such as "spooky action at a distance", only seen in quantum systems. So we can operate them, these new technologies must have a conventional - classical - IT interface. Furthermore, the quantum resources need to be controlled with classical sources, such as electromagnetic fields. However, we know that everything is actually made of quantum parts! So this begs a question: Under what circumstances are fields quantum - and thus part of the technology resources - and under what conditions are they classical - and thus part of the control interface? A "standard" answer to this question is size: A field with one photon (one quantum of light) is clearly quantum, and a large coherent field containing many photons is classical. In our work we demonstrate that the actual answer is rather more subtle than this. Indeed, it is possible to take a field with fifty or more photons in it, and allow it to be highly quantum (part of the resources), or force it to be classical (a control field) by changing its environment. So size is a factor, but it's not the only thing that matters. In the end how a system behaves is also determined by what it interacts with.

For some unknown reason I was reading up on syllogistic argument the other day and came up with this:

- All classical trajectories are deterministic (i.e. not probabilistic).
- (if there exists a correspondence limit for quantum mechanics then) Some quantum trajectories are classical (in terms of expectation values of observables).
- Hence, some quantum trajectories are deterministic (¿ in terms of expectation values of observables ?).

not sure that this is even vaguely surprising yet I get the feeling there is a mistake in the logic. If so - I would like to know where - hence posting it here for constructive criticism.

Last year at the ICTP's Workshop on Quantum Phenomena and Information: From Atomic to Mesoscopic Systems Serge Haroche presented: Reconstructing the Wigner function of photonic Schrödinger cats in a cavity: a movie of decoherence.

While this was one of the best talks of the conference I was mildly disappointed that there were no actual movies of the decoherence process. The situation has now changed with the publication of the paper below in Nature - movies of the reconstructed Wigner function are available for download on the links given below. They really are well worth a look.

Reconstruction of non-classical cavity field states with snapshots of their decoherence

Samuel Deléglise, Igor Dotsenko, Clément Sayrin, Julien Bernu, Michel Brune, Jean-Michel Raimond & Serge Haroche

Abstract

The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization, but can instead be reconstructed1 from an ensemble of copies through measurements on different realizations2, 3, 4. Reconstructing the state of a set of trapped particles shielded from their environment is an important step in the investigation of the quantum–classical boundary5. Although trapped-atom state reconstructions6, 7, 8 have been achieved, it is challenging to perform similar experiments with trapped photons because cavities that can store light for very long times are required. Here we report the complete reconstruction and pictorial representation of a variety of radiation states trapped in a cavity in which several photons survive long enough to be repeatedly measured. Atoms crossing the cavity one by one are used to extract information about the field. We obtain images of coherent states9, Fock states with a definite photon number and 'Schrödinger cat' states (superpositions of coherent states with different phases10). These states are equivalently represented by their density matrices or Wigner functions11. Quasi-classical coherent states have a Gaussian-shaped Wigner function, whereas the Wigner functions of Fock and Schrödinger cat states show oscillations and negativities revealing quantum interferences. Cavity damping induces decoherence that quickly washes out such oscillations5. We observe this process and follow the evolution of decoherence by reconstructing snapshots of Schrödinger cat states at successive times. Our reconstruction procedure is a useful tool for further decoherence and quantum feedback studies of fields trapped in one or two cavities.

It seems that this blog is being updated nowhere near as frequently as as should be. I was recently invited to give a talk at Recent Trends in Mathematical Sciences in Bahrain 2008 - giving me an ideal opportunity to add something to this page.

There were a number of excellent talks, most notable were those by Dmitri Vassiliev, Barry Sanders and Alexander Balinsky.

It is the content of the talk by Dimitri Vassiliev that I want to highlight here. On a personal note it was great to see him again - as I last saw him when he taught me as an undergraduate.

In this work Cosserat theory of elasticity was applied to the telleparalism approach of Carten and Einstein in order to try to achieve a unified field theory.

Einsiten and Carten first proposed this theory there were initially great hopes of a unified field theory - however, as they failed to produce any results - it quickly fell into disfavour. In essence Dimitri presents a promising new approach to this old idea. Here, a conformally invariant axial torsion of telleparallsim connections is used to generate a Lagrangian density. Application of the principle of least action is then applied in the usual way. Interestingly, the Lagranginan factorizes so and as a corollary we the positive and negative massless Dirac equations fall out.

Furthermore, despite the governing equations being non-linear, plane wave solutions are found to exist.

Hence, a new model for fermions (with and without mass) was presented where:

There were a number of excellent talks, most notable were those by Dmitri Vassiliev, Barry Sanders and Alexander Balinsky.

It is the content of the talk by Dimitri Vassiliev that I want to highlight here. On a personal note it was great to see him again - as I last saw him when he taught me as an undergraduate.

In this work Cosserat theory of elasticity was applied to the telleparalism approach of Carten and Einstein in order to try to achieve a unified field theory.

Einsiten and Carten first proposed this theory there were initially great hopes of a unified field theory - however, as they failed to produce any results - it quickly fell into disfavour. In essence Dimitri presents a promising new approach to this old idea. Here, a conformally invariant axial torsion of telleparallsim connections is used to generate a Lagrangian density. Application of the principle of least action is then applied in the usual way. Interestingly, the Lagranginan factorizes so and as a corollary we the positive and negative massless Dirac equations fall out.

Furthermore, despite the governing equations being non-linear, plane wave solutions are found to exist.

Hence, a new model for fermions (with and without mass) was presented where:

- space time is treated as a Cosserat continuum;
- the Lagrangian density and axial torsion are conformally invariant
- via an analogous approach to that of Kaluza & Klien; both mass and electromagnetism can be self consistently introduced to the model.

Our recent post "On non-Hermitian quantum mechanics" arXiv:0804.2051 we critique some recent work in the field by Carl Bender et al [see for example Phys. Rev. Lett 98, 040403 (2007) and Rep. Prog. Phys. 70, 947-1018 (2007)]. Their work is of interest but, in our opinion, there is some misuse of terminology with respect to the label "non-Hermitian". To us it is more like they are doing conventional quantum mechanics with novel inner products.

There already exists in the literature comments on this topic (e.g. Ali Mostafazadeh arXiv:quant-ph/0310164 and arXiv:quant-ph/0407070 as well as David B. Fairlie and Jean Nuyts arXiv:hep-th/0412148). While these papers present valid arguments they miss the central point of our comment. Namely, that if one chooses such an inner product then the Hamiltonian in question is actually Hermitian (and the whole exercise is somewhat redundant). Our argument is based on an observation that there exists in the literature some confusion over the definition of Hermiticity and the imposition of Schrödinger evolution on the evolution of state vectors. [This argument is not quite the same as the one presented in L.D. Landau and E.M. Lifshitz, “Quantum Mechanics (Non-relativistic Theory)” which, as we point out, also contains a flaw].

There already exists in the literature comments on this topic (e.g. Ali Mostafazadeh arXiv:quant-ph/0310164 and arXiv:quant-ph/0407070 as well as David B. Fairlie and Jean Nuyts arXiv:hep-th/0412148). While these papers present valid arguments they miss the central point of our comment. Namely, that if one chooses such an inner product then the Hamiltonian in question is actually Hermitian (and the whole exercise is somewhat redundant). Our argument is based on an observation that there exists in the literature some confusion over the definition of Hermiticity and the imposition of Schrödinger evolution on the evolution of state vectors. [This argument is not quite the same as the one presented in L.D. Landau and E.M. Lifshitz, “Quantum Mechanics (Non-relativistic Theory)” which, as we point out, also contains a flaw].

Labels:
non-Hermitian quantum mechanics

Just back from a great holiday that started with a 7 night cruse from Luxor to Aswan with Abercrombie & Kent. Absolutely excellent, would recommend them to anyone. Then we to Mt Siani with some good friends of ours for new year. It was there that we saw this Halo above St Catherine's monastery. Makes a rather pleasing photo, feel free to use this image to support your physics teaching if you want to (please remember to cite this blog).

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- Mark J Everitt
- Lecturer in Quantum Control, Department of Physics, Loughborough University & Lecturer in Mathematics and Physics, Centre for Theoretical Physics, The British University in Egypt