Our latest paper: The exact solution of generalized Dicke models via Susskind–Glogower operators

Our latest paper The exact solution of generalized Dicke models via Susskind–Glogower operators  has been published a day ago in J. Phys. A: Math. and Theor.  The Dicke Hamiltonian is a workhorse of Quantum Optics, it describes the interaction of a collection of identical two-level systems with a single mode electromagnetic field under the long wave and rotating wave approximations. Surely, you will be thinking: "well, that model conserves the total number of excitations and parity; then, it's trivial to find its proper values and states." Well, it is trivial to solve the system but, as far as I know, it's not that trivial to follow the dynamics of a large ensemble under this model. 

Actually, I was looking at recent solution to a nonlinear version of this model via the Bethe ansatz method and  I got frustrated that even by using this method it was hard to follow the dynamics of a qubit ensemble of size twenty. So, Héctor and I sat down and applied a right unitary method that we had used to follow the dynamics of a quantum Landau-Zener-Majorana Hamiltonian a few months ago. It was trivial to extend the approach from a single qubit to an ensemble but the solution was not elegant enough, as you can see in the first part of the latest paper. So, we tried an alternative, instead of thinking about transformations we just thought about algebraic manipulation of the Hamiltonian at hand. After a few tries, we realized that one particular arrangement allowed us to write the evolution operator as the transform operators acting on the evolution operator of a tridiagonal matrix in the ensemble basis that depended only on the number operator. From there, it was all downhill because calculating the evolution operator of such a semi-classical-like Hamiltonian is quite simple, numerically, even for very large matrices and applying the transform operators on the initial states was easier than applying them on the time evolution operator. 

At the time when we were writting the paper, I only had my dual-core i7 laptop with 8GB of RAM, but it only took a few hours to follow the dynamics of an ensemble consisting of twenty-five qubits interacting with a coherent field with as mean photon number of twenty five. Now, I have done some simulations in my eight-core i7 desktop with 64GB RAM and I can follow the dynamics of a hundred qubits overnight with a very inefficient program. I'm hoping hat I will be able to simulate four or five hundred qubits interacting with large coherent fields as soon as I have time to sit down to think about this problem again.

Oh, I forgot to tell you. Once we obtained a result for just the Dicke model we extended the approach to include independent nonlinearities in the field and the ensemble, an approach a little bit more general than that of the guys in the Bethe ansatz method.

So, I hope you like our approach, use it and cite us in the future. You can find the Journal version at JPAMG. If you don't have access, we have prepared a manuscript with the final published version but without the journal format and uploaded it to the arXiv.

Last week papers (20th week of 2012)

From May 6th to 12th, 2012, a complete mess of a week with no time for small talk about the papers. Sorry...

Published

• "Transformation design method for quantum states" by  De-Hone Lin, Physical Review A 85, 053605 (2012).


• "Testing the equivalence between the canonical and Minkowski momentum of light with ultracold atoms" by Wen-Zhuo Zhang, Peng Zhang, Ru-Quan Wang, and Wu-Ming Liu, Physical Review A 85,  053604 (2012).


• "Quantum entanglement in nanocavity arrays" by T. C. H. Liew and V. Savona,  Physical Review A 85 ,  050301(R) (2012).


• "Mechanical Evidence of the Orbital Angular Momentum to Energy Ratio of Vortex Beams" by C. E. M. Demore et. al.,  Physical Review Letters 108 ,  194301 (2012).
    

Preprints

• "Quantum phase transition in the Dicke model with critical and non-critical entanglement" by L. Bakemeier, A. Alvermann and H. Fehske, arXiv: 1204.4974v1 [quant-ph].
  
  

Last week papers (19th week of 2012)

It has been an awful busy short week, I can barely keep my eyes open. This week from April 29th to May  5th 2012, I will point out the articles that caught my attention, I'm sorry for the lack of comments...

Published

• "Quantum Rabi model for N-state atoms " by  V. Albert, Physical Review Letters 108, 180401 (2012).
  
  
  
  


• "Acoustic analogue of graphene: Observation of Dirac cones in acoustic surface waves" by D. Torrent and J. Sánchez-Dehesa, Physical Review Letters 108,  174301 (2012).
  
  
  
  


• "Encoding relativistic potential dynamics into free evolution" by C. Sabín et. al., Physical Review A 85,  052301 (2012).
  
  
  


• "Super diffusion in optical realizations of Anderson localization" by Y. Krivolapov et. al., New Journal of Physics 14, 043047 (2012).
  
  
  
  


• "Simple derivation of the Lindblad equation" by P. Pearle, European Journal of Physics 33,  805 (2012).
  
  
  
  

Preprints

• "Multipartite optomechanical entanglement from competing nonlinearities " by A. Xuereb et. al., arXiv: 1204.4974v1 [quant-ph].
  
  
  
  

Last week papers (18th week of 2012)

From 22 to 28 of April 2012, well it was really from 22 to 26 as I took a long weekend off the office...

Published

• "Quantum Computing with Incoherent Resources and Quantum Jumps" by  M. F. Santos et. al., Physical Review Letters 108, 170501 (2012).
  
  
  So, let us say that you have logarithmic spare time and want to make nature do computation for you. Well, Marcelo and coauthors have just show that, in principle, you just need time, patience, clickers and a way to put/remove them clickers from your open system. 


• "Optical Forces and Torques in Nonuniform Beams of Light" by D. B. Ruffner and David G. Grier, Physical Review Letters 108,  173602 (2012).
  
  
  I don't remember seeing an optical tweezer paper in PRL. The authors analyze linear and angular momentum densities of light beams to show how amplitude, phase and polarization profiles contribute to optical forces. One interesting thing they found is how the curl of the spin angular momentum can exert torque on objects without contributing to the orbital angular momentum of the beam. 


• "Equilibrium and disorder-induced behavior in quantum light–matter systems" by E. Mascarenhas et. al., New Journal of Physics 14,  043033 (2012).
  
  Coupled two-level system cavity arrays in the polaritonic regime have been proposed to realize the Bose-Hubbard model and Insulator-Superfluid transition  in the past. Now, by using a mean field approach the authors study the effects of disorder on the phases of the Jaynes-Cummings-Hubbard model and find glassy phases using entanglement measures. Interesting, ain't it?  

Preprints

• "Supermodes of Hexagonal Lattice Waveguide Arrays" by J. S. Brownless et. al., arXiv: 1204.4974v1 [quant-ph].
  
  
  A modal approach to hexagonal  photonic waveguide arrays. I'm still trying to follow it and get their results and see if it helps me solve some other waveguide lattices.


• "Relating the quantum mechanics of discrete systems
  to standard canonical quantum mechanics" by G. Hooft , arXiv: 1204.4926v1 [quant-ph].
  
  So, imagine you are working near the Planck scale and you want to see if there's something happening there, most probably you want to go from continuous to discrete modelling of the system. Well, here's an approach focused on applications to the harmonic oscillator. I need time to sit down and follow this, discrete dynamics is always interesting for me.


• "Dynamical scattering models in optomechanics: Going beyond the `coupled cavities' model" by A. Xuereb and P. Domokos  , arXiv: 1204.5301v1 [quant-ph].
  
  
  An analysis of membrane-coupled cavities from first principles. In short, we are safe using the coupled-cavities simplification if the coupling element reflectivity is not way below 50% .


• "Morse potential derived from first principles" by R. Costa Filho et. al., arXiv: 1204.5931v1 [quant-ph].
  
  I .

Last week papers (17th week of 2012)

Without further ado...

Published

• "Quantum phase transition in the Dicke model with critical and noncritical entanglement" by  L. Bakemeier, A. Alvermann and H. Fehske, Physical Review A 85, 043821 (2012).
  
  
  A phase transition analysis on the Dicke model exploring the behavior of the system when the frequency of the field mode tends to zero, called the classical oscillator limit by the authors, where the model goes to a Lipkin-Meshkov-Glick model. Why people don't cite us? Really... 

• "Ultimate limits to quantum metrology and the meaning of the Heisenberg limit" by M. Zwierz, C.A. Perez-Delgado and Pieter Kok, Physical Review A 85,  042112 (2012).
  
  
  I remember being at a seminar where Carlos presented this work in CQT. It's a mashup of query complexity with quantum mechanics to reformulate a Heisenberg limit for quantum metrology based on the idea of physical resources. 

• "Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model" by Christian Nietner and Axel Pelster, Physical Review A 85,  043831 (2012).
  
  
  As  you know, I like anything Jaynes-Cummings or Dicke. A while ago some people decided to study what happens when you couple cQED building blocks (cavities with an atom inside) and used a polaritonic approach to the problem to describe an isulator and superfluid phase of the system. So, it is nice that a phenomenological theory of superconductivity is used to describe the superfluid phase of the system! 

Preprints

• "Non-Markovian quantum dynamics and classical chaos" by I. Garcia-Mata, C. Pineda and D. Wisniacki, arXiv: 1204.3614v1 [quant-ph].
  
  
  The authors study a system coupled to an environment with different levels of chaos and analyse how well a chaotic environment models Markovian evolution.


• "Theory of optomechanics: Oscillator- eld model of moving mirrors" by C.R. Galley, R.O. Benhunin and B.L. Hu, arXiv: 1204.2569v1 [quant-ph].
  
  
  A nice theory of coupling between a field and a moving mirror from first principles that converges to models used in the literature. I was more interested in the convergence to what they called the N x coupling that we widely use in Quantum Optics.


• "Superradiant quantum phase transition in a circuit QED system: a revisit from a fully microscopic point of view" by D.Z. Xu, Y.B. Gao and C.P. Sun, arXiv: 1204.2602v1 [quant-ph].
  
  
  The authors derive the Dicke Hamiltonian from a microscopic model circuit-QED involving superconducting qubits and a quantized field. These model allows for a so-called superradiant phase transition in contrast to a previous analysis in the literature.


• "Exact solution to the quantum Rabi model within Bogoliubov operators" by Q.H. Chen, C. Wang and K.L. Wang, arXiv: 1204.3668v1 [quant-ph].
  
  It is a nice step by step demonstration of how to get a exact solution for the quantum Rabi model with an additional tunneling. The authors recover Braak's solution. I personally love the closing paragraph.

The Russian Solution to the quantum Rabi Model

There's a frightful phrase in physics that goes "a Russian solved it a while ago."

A while ago a very nice paper of D. Braak appeared discussing the integrability of the quantum Rabi Model in Physical Review Letters. This is a nice elegant paper using a discrete symmetry to show that the model is  integrable and gives an exact spectrum for the model [Phys. Rev. Lett. 107, 100401 (2011)].  

The one interesting thing is that the spectrum for the quantum Rabi model was shown by É. A. Tur by resolvent theory eleven years before [Optics and Srectoscopy 89, 574-588 (2000) (English) Optika i Spektroskopiya 89, 628-642 (2000) (Russian)]. If someone can find a pdf file please email it to me, I could only get a bad scan of a battered photocopy.

And don't get me wrong, Braak's paper contribution goes beyond the spectrum. He explores the implications that symmetries has on integrability for models that doesn't have a classical limit/analogue.

Also, a little bit further in time, J. Casanova et. al. analyzed the spectra and dynamics of the quantum Rabi model in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 (2010)] and presented an approximated spectra for the model and the curious collapse and full revival of the ground state of the positive parity chain.

Again, that particular oscillatory behavior for the same state was discussed by É. A. Tur but for weak coupling in [Optics and Spectoscopy 89, 574-588 (2000) (English) Optika i Spektroskopiya 89, 628-642 (2000) (Russian)] and an elegant approximation to the spectra leading to their result in [arXiv: 0211055 [math-ph]].

And don't get me wrong again, Casanova et. al. study the deep ultrastrong coupling and delve in the analysis they are presenting by adding a phase space analysis and some numerical analysis on the topic.

My point is that some of the results in both Physical Review Letters has been known for ten years already and nobody cited the work of É. A. Tur. A simple Google search of "Jaynes-Cummings model  without rotating wave approximation" brings Tur's paper in the second place, did the editors or reviewers even bother?

Now, surely there's a dozen papers in the review queue that are working on the topic and citing Braak and Casanova—which is the right honest thing to do—but is someone citing Tur? Show the guy some love, his work is nice, clean and elegant.


Edit: I forgot to mention that Tur's result was for weak coupling, g=0.5.

Last week papers (16th week 2012)

Now, Happy belated easter; writing in advance is really confusing because today is the first week of Easter and this will not see light until the second... and I'm rambling... back to business, the interesting things on the physics 'tubes from April 9th to 15th...

Published

• "Observation of the Kinetic condensation of classical waves" by  C. Sun,  et. al., Nature Physics (2012).
  
  
  This I want to read, a few years ago I think I saw a paper on the topic—give me a second...this one and this one in PRL—and it really got my eye. Now, that's something I want to learn about, it seems fun and interesting.

• "Tavis-Cummings model beyond the rotating wave approximation: Quasidegenerate qubits" by S. Agarwal, S.M. Hashemi Rafsanjani and J. H. Eberly , Physical Review A 85,  043815 (2012).
  
  
  As Rabi model has come back, it was not long before the many two-level system version should appear back in press. Here the dynamics in a particular regime where the energy gap of the two-level system  is way smaller than the frequency of the field is explored with strong coupling via an adiabatic approximation known for the same regime but for a single two-level system interacting with a field.

Preprints

• "Can free will emerge from determinism in quantum theory?" by G. Brassard and P. Raymond-Robichaud et. al., arXiv: 1204.2128v1 [quant-ph].
  
  
  They push a deterministic, local and realistic interpretation of quantum mechanics, this never gets old at all and now we have a "parallel lives" added to the zoo of interpretations. If you like interpretations, philosophical speculation and so, this is for you  


• "Producing and measuring entanglement between two beams of microwave light" by E. Flurin et. al., arXiv: 1204.0732v1 [quant-ph].
  
  
  I'm too lazy to read it today but entanglement between beams of microwave is interesting. 


• "Thermal phase transitions for Dicke-type models in the ultra-strong coupling limit" by M. Aparicio Alcalde et. al., arXiv: 1204.2271v1 [quant-ph].
  
  
  I like almost everything related to Dicke model, here a study of thermal phase transitions of the mathematical model is presented. I like papers involving Emary and Brandes, they are nice reads.

Last week papers (15th week 2012)...

I told you about the Nature Physics Insight on Quantum Simulation, so I will skip those 

Published

• "Ultra-high Q mechanical oscillators through optical trapping" by  D. E. Chang,  et. al., New Journal of Physics 14, 045002(2012).
  
  
  This is interesting: Reaching the quantum ground state of a mechanical oscillator at room temperature.The authors propose the use of optical forces to free a the characteristics of a mechanical structure from its material properties.

• "Collapse-revival dynamics and atom-field entanglement in the nonresonant Dicke model" by A. Alvermann, L. Bakemeier and H. Fehske, Physical Review A 85,  043803 (2012).
  
  
  A numerical studies of Rabi model, it's all coming back again and again and again. They study collapse and revivals out of resonance. 


• "Stimulated Emission from a Single Excited Atom in a Waveguide" by E. Rephaeli and S. Fan, Physical Review Letters 108, 143602 (2012).
  
  
  It's stimulated emission in a single-atom confined in a waveguide scenario. .


• "Uncertainty Relation for Photons" by I. Bialynicki-Birula and Z. Bialynicka-Birula,   Physical Review Letters 108, 140401 (2012).


Can you tell that I don't really want to write anything?

  
• "Solvability of the two-photon Rabi Hamiltonian" by I. Travenec, Physical Review A 85, 043805 (2012).
  
  
  I told you, it's the Rabi model again and again and again... here with two-photon transitions instead of one-photon.

  
• "Widely Tunable, Nondegenerate Three-Wave Mixing Microwave Device Operating
  near the Quantum Limit" by N. Roch et. al., Physical Review Letters 108, 147701 (2012).
  
  
  Now, the best for the last. I find this awesome, people are making better and better microwave resonators, emitters and now it is possible to do three-wave mixing in the microwave regime!

Preprints

• "Entanglement control in hybrid optomechanical systems" by B. Rogers et. al., arXiv: 1204.0780v1 [quant-ph].
  
  
  I'm too lazy to read it today but seems quite interesting...  


• "Producing and measuring entanglement between two beams of microwave light" by E. Flurin et. al., arXiv: 1204.0732v1 [quant-ph].
  
  
  I'm too lazy to read it today but entanglement between beams of microwave is interesting. 

It's Quantum Simulation issue in Nature Physics Insight!

I can tell you that this is one of  Feynman's most beautiful phrase and I use it as often as possible in my presentations as opening slide:

 “Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.”

That's the opening phrase for Trabesinger's editorial on the current issue of Nature Physics that includes a commentary by Cirac and Zoleer and reviews by Bloch, Dalibard & Nascimbéne, Blatt & Ross, Aspuru-Guzik & Walther, and Houck, Tureci and Koch.

Enjoy! I know I will...

Last Week Papers (14th week 2012)

It feels good to be back in an office and able to follow the literature. I'm thinking that I like the list format and now will split it in two: published and pre-prints because it is good to talk about pre-prints.

Published

• "Quantum Interface between an Electrical Circuit and a Single Atom" by  D. Kielpinski,  et. al., Physical Review Letters 108, 130504 (2012)
  
  
  They have shown it may be possible to couple an ion to a quantized current from a superconducting circuit. That's nice as the experiments in classical coupling of currents and ions can be used to build upon them and get to this. Interesting read.

• "Optical Detection of the Quantization of Collective Atomic Motion" by N. Brahams et. al., Physical Review Letters 108, 133601 (2012).
  
  
  They are measuring the collective motion of a gas coupled to a cavity field. That impresses me.


• "Superradiance in spin- j particles: Effects of multiple levels" by G._D Lin and S. F. Yelin, Physical Review A 85, 033831 (2012).
  
  
  It has always been a problem to talk about superradiance in two-level systems. Physically sound models with two-level systems involve Raman pumping to auxiliary levels in 4-levels schemes. It has always been mentioned that it may be possible to have superradiance with multi-level atoms. Well, they calculate it and show the effect of multi-level atoms in radiance, decay and so on...


• " A heuristic approach to BEC self-trapping  in double wells beyond the mean field" by K. Rapedius,  Journal of Physics B: Atomic, Molecular and Optical Physics 45, 085303 (2012).


A semi-classical analysis of the Bose-Hubbard dimer Hamiltonian with some curious variations that seem to help producing some approximations that may be valid in the mean-field and finite particle number cases.

  
• "Effects of orbital angular momentum on the geometric spin Hall effect of light" by L.-J. Kong, Physical Review Letters 85, 035804(2012).
  
  
  Reading it and trying to figure it out... I have never read about the spin Hall effect of light and it seems like there are two different kinds: one at a gradient refractive index interface and another that is geometric and relates to observation from a frame tilted with respect to the propagation direction. I need to read more about all this things.

Preprints

• "Exact real-time dynamics of the quantum Rabi model" by F.A. Wolf, M. Kollar, and D. Braak, arXiv: 1203.6039v1 [quant-ph].
  
  
  Last year Braak wrote a very nice PRL where he presented the proper system of Rabi model; now, this follow-up paper builds upon the basis presented before and analyses the dynamical behavior in different time regimes. I wonder why nobody cites E. A. Tur's papers on approximations to the eigenvalues of Rabi model. Anyway,  This manuscript is quite interesting and a must read if you work in Quantum Optics.  


• "Quantum thermometry using the ac Stark shift within the Rabi model" by K.D.B. Higgins, B.W. Lovett, and E.M. Gauger, arXiv: 1203.5994v1 [quant-ph].
  
  
  I have the feeling that whenever I get to grasp what they are doing I'm gonna like it.

Last Week Papers (13th week 2012)

I'm back from vacations and trying to catch up with the quantum optics pile of papers that came out in those two weeks. Here're some of the articles that caught my eye:

• "An analysis of the changes in ability and knowledge of students taking A-level physics and mathematics over a 35 year period" by Peter J Barham, Physics Education 47, 162-168 (2012).
  
  I loved the closing phrase, I cite: "The change in mathematical ability makes teaching physics at degree level more challenging, but that is a challenge we should embrace, rather than simply protest about."


• "Extracting Dynamical Equations from Experimental Data is NP Hard" by Toby S. Cubitt, Jens Eisert, and Michael M. Wolf, Physical Review Letters 108, 120503 (2012).
  
  In other words, it is damn hard to figure out the underlying math just from experimental data. The result is nice to read and quite interesting.


• "Cooling by Heating: Refrigeration Powered by Photons" by B. Cleuren, B. Rutten, and C. Van den Broeck, Physical Review Letters 108, 120603 (2012).
  
  This is interesting, you can cool a lead by joining it to another lead through two quantum dots. There was another interesting paper in the same issue about cooling with incoherent light but I seem to have misplaced it on my files.


• "Generation of Mesoscopic Entangled States in a Cavity Coupled to an Atomic Ensemble" by G. Nikoghosyan, M. J. Hartmann, and M. B. Plenio, Physical Review Letters 108, 123603 (2012).
  
  Something like dark states but by using 6-level atoms.


• "Controlled Dicke Subradiance from a Large Cloud of Two-Level Systems" by Tom Bienaime, Nicola Piovella, and Robin Kaiser, Physical Review Letters 108, 123602 (2012).
  
  Everybody was talking about Dicke super-radiance two years ago, now it is time for Dicke subradiance to be shown experimentally and used to control storage in long-lived subradiant modes

LWP: A list of papers (On vacation)

I'm really getting into the on vacation mood, my google reader rss feed list has some 1300 unread articles from my favorite journals and I don't even have plans to even take a look at them for another two weeks. Nevertheless, this one caught my eye when I opened the google reader last time (disclosure: they cited a paper of us, that's why it caught my eye):

Polariton condensation with nonlinear photons by X.-Y. Guo, Z.-Z. Ren and Z. Chi, Physical Review A 85, 023608 (2012).

From the abstract, I have the feeling I'm gonna read it, like it, and maybe do something based on this in the future... or maybe not as I'm starting to feel a calling for something different in the optics/professional-life front.

LWP: A list of papers (on vacation)

I'm really getting into the on-vacation mood and not even worrying about checking the RSS feeds for my favorite journals everyday (I think my google reader has some 800 unread items as of today). Last week, I managed to skip through the feed and found these interesting:

Anderson localization in a periodic photonic lattice with a disordered boundary by  U. Naether, J. M. Meyer, S. Stützer, A. Tünnermann, S. Nolte, M. I. Molina, and A. Szameit, Optics Letters 37, 485-487 (2012).


Optomechanical cooling of levitated spheres with doubly resonant fields by G. A. T. Pender, P. F. Barker, F. Marquardt, J. Millen, and T. S. Monteiro, Physical Review A 85, 021802(R) (2012).


Optomechanical systems as single-photon routers by G. S. Agarwal and Sumei Huang, Physical Review A 85, 021801(R) (2012).

I hope I can read them sometime in the future after this lackadaisical bought of laziness.

LWP: A list of papers (On vacation)

I am taking my vacation seriously and just reading titles and abstracts. These caught my eye, I hope I will read them whenever I'm back:

Transverse and lateral shifts of the center of gravity of a refracted nonparaxial Bessel beam by E. Norblad, Physical Review A 85, 013847 (2012).

Reflectivity and transmissivity of a cavity coupled to two-level systems: Coherence properties and the influence of phase decay by B. Julsgaard and K. Mølmer, Physical Review A 85, 013844 (2012).


Cavity cooling of a trapped atom using electromagnetically induced transparency by M. Bienert and G. Morigi, New Journal of Physics 14, 023002 (2012).


An optical-lattice-based quantum simulator for relativistic field theories and topological insulators by L. Mazza, A. Bermudez, N. Goldman, M. Rizzi, M. A. Martin-Delgado and M. Lewenstein, New Journal of Physics 14, 015007 (2012).

That's it...

LWP: Quantum memory with a single two-level atom in a half cavity

by Y. Wang, J. Minar, G. Hetet, and V. Scarani.
Physical Review A 85, 013823 (2012)

Wang and collaborators show that it is possible to store a single-photon pulse in a two-level atom within a half cavity setup where the decay rate between the atom and the light is controlled by motion of the one mirror in the half cavity.

A dipole-field interaction leading to optical Bloch equations from Heisenberg picture is used; the effects of the half-cavity are encoded in a term accounting for decay  into the half-cavity (pulse) mode, decay and noise introduced by the environment are also taken into account. Assumptions include: Markov approximation (long half-life times compared to light's round-trip between atom and mirror), small mirror motion (of the order of a wavelength) leading to neglect amplitude changes in time scales smaller or equal to a round-trip time—but this cannot be assumed in the phases due to the importance of interferences in the sysme— 

The probability of the two-level system absorbing a single-photon wave packet is found and a suitable decay function is given that maximizes such probability. Storage is achieved by placing the atom at a node of the half-cavity system. Then, the emission efficiency is calculated and a decay rate is defined which controls the temporal shape of the outgoing single-photon pulse. The authors present simulations for a sampling of time-bin single-photon pulses and their respective control decay-rate leading to high fidelity storage and possible implementations of their protocol.

The article is didactic in its presentation and the topic is quite interesting. I was not familiar with half-cavity schemes and this manuscript presents a nice survey of references in the topic. I hope experiments using their protocol follow soon.

LWP:Absence of vacuum induced Berry phases without the rotating wave approximation in cavity QED

by Jonas Larson
Physics Review Letters 108, 033601 (2012)

Some ten years ago, Berry phase was studied in the Jaynes-Cummings model. In this paper, Larson focuses on proving that such a geometric phase arises from the use of the rotating wave approximation.

First, Larson reviews the results fro the Jaynes-Cummings model, that is, under the rotating wave approximation, and derives the accumulated Berry phases by exact diagonalization of the Hamiltonian. Then, he presents a semiclassical approximation derivation by using canonical operators for the field and Born-Oppenheimer approximation to obtain a pair of adiabatic potentials that lead to semiclassical conical energy surfaces giving a Berry phase which is identical to that given by the exact calculation for large photon number. 

Once the validity of this semiclassical approximation is provided by this example, Larson uses the same method to find the semiclassical energy surfaces for the case without the rotating wave approximation, that is, Rabi Hamiltonian, and shows that these surfaces lack the conical intersection that gives a non zero Berry phase. Actually, the semiclassical energy surfaces for this case intersect along the line given by x=0 instead of just a point. It is noted that the author carried a numerical diagonalization of the Hamiltonian and the results were confirmed.

Furthermore, Larson revisits a lambda-atom configuration where a Raman coupling scheme is used and shows that by assuming far detuned driving fields such that adiabatic elimination can be carried on, without any rotating wave approximation, the semiclassical energy surfaces for the system do not intersect at a single point and Berry phase must be zero all the time.

He also discusses the case of a single atom in a bichromatic cavity and shows that within the used semiclassical formalism there are no vacuum induced Berry phases. A trio of other systems are presented with the same result: no Berry phase when the rotating wave approximation is not used.    

It concludes, that the presence of a Berry phase in the Rabi model and other models discussed (adiabatic elimination, bichromatic cavities, etc) in the paper is a result of introducing the rotating wave approximation and not inherent to the models. Thus, a flag is raised: whenever Berry phase is the subject of study one has to be mindful of the approximations used independently of the coupling regime at hand. It may be even possible that this result may change if a multi-level approximation is taken instead of the typical two-level restriction of the Rabi model. It also points the interest of studying vacuum induced Berry phase in nonadiabatic processes. 

This is a very nice paper to read, it presents a concrete, straight to the fact introduction of geometrical phases in cavity-QED and the results are presented in a clear manner. If you are a fan of the Jaynes-Cummings model, you cannot leave this article unread.

LWP: Polariton Mott insulator with trapped ions or circuit QED

by M. Hohenadler, M. Aichhorn, L. Pollet and S. Schmidt
Physical Review A 85, 013810 (2012)

The authors address an extended Jaynes-Cummings-Hubbard model where photons in 1D or 2D arrays of coupled resonators—each of them holding a two-level system—can hop beyond nearest neighbors. This particular model is of relevance in circuit-QED—where 1D and 2D arrays of qubit+stripline resonators can capacitively couple—and in trapped ions&mdahs;where dipole interactions are long range—. So, the model are basically 1D or 2D arrays of polaritons—qubit+fied excitation—with short and long range coupling.

They study a 1D frustrated long-range hopping model in the context of trapped ions and the same in 2D by assuming a circuit-QED model. The first is studied using a variational cluster approach and a quantum Monte Carlo method (ALPS 1.3 implementation), the second only the quantum Monte Carlo method. Analytically, Metzner's local cumulants are used to calculate a photonic Matsubara Green's function for the system within a random phase approximation.

The authors find a Mott-superfluid transition by changing the hopping to qubit-field coupling ratio as usual with these models. Their results show that the Mott lobes characteristic for this transition are enlarged/reduced in the case of trapped ions/circuit-QED but they realize that neither the quantum Monte Carlo, nor the variational cluster approaches provide any evidence of a change of the universality class of phase transition in the presence of long-range hopping.

This is one of those papers that would take long to duplicate but are nice to read and learn the physics of the studied system and even more interesting if you like anything Jaynes-Cummings.

LWP: Optical Thomas-Reiche-Kuhn sum rules

by S. M. Barnett and R. Loudon
Physical Review Letters 108, 013601 (2012)

Thomas-Reiche-Kuhn sum rules are quite important in Quantum Optics, they tell us that the sum of squared dipole moments from a any given energy level is constant in the dipole approximation. They have been useful in providing a validity check in radiation-matter interaction, like no-go theorems in the case of super-radiance in Dicke model. Anyhow, it is a necessary condition for the canonical commutation relation between position and momentum of an atomic electron to hold.

In their article Barnett and Loudon—who, by the way, have written very useful and didactic books in Quantum Optics each—explore the electromagnetic field in lossless magnetodielectric media and show that the equal-time commutation relations for the four electromagnetic field operators deliver four polariton sum rules (for the unity, permittivity, permeability and their product) analogous to the atomic Thomas-Reiche-Kuhn sum rule. They show a proof of these optical TRK sum rules by analysing the case where complex polariton frequencies are restricted to the lower half complex plane; the proof is beautiful and simple, they use complex variable analysis to state the fact that path integration in the half-upper complex planes for the four complex functions is equal to one as both the permittivity and permeability goes to one as the frequency goes to infinity, then, in the lower half, the contour integral is calculated from the zeroes of each of the four quantities corresponding to solutions of the dispersion relation for polaritons in a lossless magnetodielectric mediuml; this delivers a residue equal to one. Finally, by using a relation between residues and derivatives of the dispersion relation, they show that this residue is actually a sum over the polariton phase velocities, a little bit more of algebra and tada! They also sketch the effect of losses but leave it for a following article.

They results indicate that it is not possible to design a medium where all polariton modes are in the negative-index region. Interesting for all the meta-material research. I'm curious how this comes out in the presence of losses.

Man, oh man. I'm really dusted in complex variable. I'm still half-way in the calculations, but the paper is so beautiful written that everything seems so logical and simple.

LWP: Dicke Quantum Spin Gas of Atoms and Photons

by P. Strack and S. Sachdev
Physical Review Letters 107, 277202 (2011)

A few years ago, Nagy and collaborators proposed to use Dicke model to describe atoms in a quantized cavity driven by a classical field in one-dimension [Eur. Phys. J. D, 2008, 48, 127 - 137]. Later Baumann and collaborators experimentally demonstrated a checkerboard transition in the two-dimensional center of mass motion  of a condensate in a cavity and an optical lattice which may be described by Dicke's model [Nature, 2010, 464, 1301 - 1306]; see also Nagy and collaborators [Phys. Rev. Lett., 2010, 104, 130401]. The experiments of Baumann and collaborators realized a supersolid atomic phase with long range interactions mediated by photons. Theoretically, Dicke's model in the thermodynamic limit (the number of two-level atoms, a.k.a. qubits, is infinitely large)  looking just at the atoms delivers a phase transition in the ground state into a ferromagnet-like structure.

Here, Strack and Sachdev study what happens in Dicke model when multiple electromagnetic modes interact with the atomic ensemble without the rotating-wave-approximation instead of just the single-mode. They propose to integrate out the photonic degrees of freedom in a path integral representation to obtain a  Hamiltonian similar to the Ising model in a transverse field, where long range interactions depend inversely on the imaginary frequencies of the qubits in the path integral. They mention that such a condensed matter model is similar to the Hopfield model and allows for Mattis ground states which critical properties should be similar to those of a single-mode Dicke model but focus on the case where the long range interaction distribution is Gaussian. This, in the infinitely large number of qubits limit, allows for an extra ground state quantum spin-glass phase appart from the paramagnet and the ferromagnet known in the single-mode Dicke model. They also show that it is also possible to calculate the photon correlation function. But most importantly, discuss that the paramagnet to ferromagnet phase transition is to be considered classical while the transition to a quantum spin-glass is a genuine phase transition from the radio-frequency spectral response function of the qubits (there is a spectral weight going to zero for a continuum of frequencies in the latter case).

I really liked the paper, it is very interesting how a well-known model still delivers new ways of studying condensed matter phenomena in quantum optics setups. I'm still trying to work my way with the formalism they used to integrate out the photon fields but the good thing is that they present the procedure in the last two pages of the manuscript and it is being very helpful.

Note: I'm sorry for the one-day delay, yesterday was a public holiday and I was lazy enough to stay at home.

LWP: On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing

by T. Gerrits et. al.
Physical Review A 84, 060301(R) (2011)

Some of the big problems in commercial realizations of Quantum Optics protocols are the inefficient coupling between systems and detectors and the forest of optical devices needed to realize them in the laboratory. Integration in optical circuits could resolve both.

This article shows a realization of a photon-number-resolving detector that can be integrated with superconducting devices in photonic circuits. The detector is a transition-edge sensor made of tungsten evanescently coupled to the system to measure.

I'm not that bright to understand everything about the technical stuff but I find this very interesting in the sense that now they can strongly increase the efficiency of their detection process and as well as resolve photon number in the system (they tested their detection scheme with a coherent pulse with a few photons)

I wish I could say more, but I am far from my lab days. It is a nice paper presenting something that may very useful in the near future go and have a look and maybe you could come back and tell me more about it.