# Breaking barriers: photon-blockade breakdown from the few quanta to the thermodynamic limit

This is a Perspective on "Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition" by A. Vukics, A. Dombi, J. M. Fink, and P. Domokos, published in Quantum 3, 150 (2019).

By Ricardo Gutiérrez-Jáuregui (Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA).

Photon blockade has become an iconic example of quantum optics in the strong coupling regime, where coherent dynamics dominate over dissipation, and properties that we have come to associate with the quantum can be unveiled. It describes the transport of light through a nonlinear optical system which, upon the absorption of a single photon, reflects the rest of the incoming light. The barrier blocking the transport of photons, however, can be surpassed. As the incoming photon flux is increased, the system re-organizes to create paths for light to cross. This organization occurs in analogy with phase transitions in thermal equilibrium, an analogy that Vukics and collaborators have set to understand in detail on their recent article [1]. The authors build upon previous studies of the breakdown of the photon blockade phase transition [2,3] to create a clear and complete picture of the steady-state behaviour across the parameter space. They explore the connection to first-order phase transitions when incoming and cavity photons differ in frequency, and, in the process, answer questions regarding the role of fluctuations both as the organizers of the steady-state and as indicators of the statistics of the detected light. Ultimately, the authors explain how the discrete spectrum of an underlying quantum system can lead to the coexistence of both quantum and classical light in blockade systems and the fate of this coexistence as the effect of fluctuations is affected by increasing photon numbers.

The analogy between phase transitions in thermal equilibrium and the abrupt change found in driven optical systems has a long history that can be traced to the early days of the laser [4]. It lead to active research throughout the 1970s and 1980s, but, as experiments started to dwelve into the strong coupling regime, fundamental issues arose. While a conventional laser depends on the emission from a large number of atoms, what sense does it make to talk about threshold behaviour when the system is reduced to just a few or even a single atom? This question points towards two points. First, quantum phase transitions are grounded in a recognizable physical process, $\textit{e.g.}$ a steep increase in photon flux or a gap in energy. Second, a thermodynamic limit can be defined as a limit of high excitation number where the effect of fluctuations can be neglected. Blockade systems provide insight into both points, since they can consist of just a single atom blocking the passage of many photons [5,6]. It has been shown that when the incoming photons match the frequency of the cavity, the breakdown of this barrier corresponds to a collapse of the energy levels of the cavity field-atom system [2,7]. In a remarkable previous experiment [3], this collapse was shown to be accompanied by changes in photon flux, going from zero when being reflected to thousands when allowed to pass. So, in this case a single system acts as a mediator for the light to interact. The transition is underlined by a collapse of energy levels and signalled by the output photons. For large coupling strengths and incoming photon flux, the same behaviour is obtained but with photons numbers rescaled, going from thousands to millions and keep on growing, smoothing-out thresholds and erasing the effect of single fluctuations. A limit of infinite photon number might be unphysical, but the idea of thermodynamic limit is maintained.

Now Vukics and collaborators return to the photon-blockade problem, but instead of being armed with their experimental set up, they are armed with simulated data obtained from quantum trajectory theory [8]. The simulated data represent photon measurement records and allows them to move across the parameter space; looking for the self-similar behaviour to connect the few quanta and thermodynamic limits.

### ► References

[1] A. Vukics, A. Dombi, J. M. Fink, and P. Domokos, Quantum 3, 150 (2019) 10.22331/​q-2019-06-03-150.
https:/​/​doi.org/​10.22331/​q-2019-06-03-150

[2] H. J. Carmichael, Physical Review X 5, 031028 (2015) 10.1103/​PhysRevX.5.031028.
https:/​/​doi.org/​10.1103/​PhysRevX.5.031028

[3] J. M. Fink, A. Dombi, A. Vukics, A. Wallraff, and P. Domokos, Phys. Rev. X 7, 011012 (2017) 10.1103/​PhysRevX.7.011012.
https:/​/​doi.org/​10.1103/​PhysRevX.7.011012

[4] R. Graham and H. Haken, Z. Physik 213, 420 (1968) 10.1007/​BF01405384.
https:/​/​doi.org/​10.1007/​BF01405384

[5] A. Imamoḡlu, H. Schmidt, G. Woods, and M. Deutsch, Physical Review Letters 79, 1467 (1997) 10.1103/​PhysRevLett.79.1467.
https:/​/​doi.org/​10.1103/​PhysRevLett.79.1467

[6] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup and H. J. Kimble, Nature 436, 87–90 (2005) 10.1038/​nature03804.
https:/​/​doi.org/​10.1038/​nature03804

[7] P. Alsing, D. -S. Guo, and H. J. Carmichael, Physical Review A 45, 5135 (1992) 10.1103/​PhysRevA.45.5135.
https:/​/​doi.org/​10.1103/​PhysRevA.45.5135

[8] L. Tian and H. J. Carmichael, Physical Review A 46, R6801(R) (1992) 10.1103/​PhysRevA.46.R6801.
https:/​/​doi.org/​10.1103/​PhysRevA.46.R6801

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