Single-Atom Lasers

Traditional lasers rely on large numbers of atoms to amplify light. In this study, we show how a single atom in an optical cavity can emit light with traditional laser behavior. Overall, this work shows how laser behavior can emerge from the smallest possible system, helping us understand where the boundary lies between quantum and classical light sources.

where the terms describe the cavity decay, incoherent pumping, and spontaneous emission (random scattering of light). Overall, this equation tells us how the system evolves over time. When we expand this equation for a three-level atom, we are left with 19 terms. We set them each to zero, and plug in the constant parameters of our system to get a matrix of solutions describing the system's behavior. We repeat this process for different photon numbers to compare behavior in three regimes:

• Low Photon Number (1 photon)

• Intermediate Photon Number (2-15 photons)

• High Photon Number (>15 photons)

We use our solutions to find the mean cavity photon number, population inversion (proportion of atom in the metastable state compared to the ground state), and the difference between stimulated and spontaneous emission rates. Stimulated emission is the coherent laser light which must dominate over the spontaneous, random scattering of light in order for us to classify our system as a laser. When the difference is negative, spontaneous emission dominates, and when the difference is positive, stimulated emission dominates and the lasing threshold has been crossed.

To provide additional evidence that confirms the emergence of laser behavior, we use the Mandel Q parameter, another way to classify the type of light being produced. We also use the Wigner function and phase-space representation to confirm what energy levels the cavity photons are populating and further classify the emitted light.

Our research has confirmed that a laser can be created from a single atom, and shows that at least 3 photons are required to be in the cavity to create the laser. It also shows that the laser begins to break down when there are more than 10 photons in the cavity. Looking at the semi-classical regime, we can conclude that the laser completely self-quenches at an incoherent pumping rate of 65. 

Potential ideas for future study: 

• Analyzing how different parameter values, such as the coupling strength or leakage rate, change our results

• Determining the largest number of photons that can be in the cavity before the laser is destroyed

• Y. Mu and C. Savage, One-atom lasers, Physical Review A 46, 5944 (1992).

• J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Experimental realization of a one-atom laser in the regime of strong coupling, Nature 425, 268 2003).

• H. Walther, Cavity quantum electrodynamics, in Encyclopedia of Optical and Photonic Engineering (Print)-Five Volume Set (CRC Press, 2015) pp. 231–239.

• A. Sokolova, D. Kalacheva, G. Fedorov, and O. Astafiev, Overcoming photon blockade in a circuit-qed single-atom maser with engineered metastability and strong coupling, Physical Review A 107, L031701 (2023).

• C. A. Potts, W. J. Franse, V. A. S. Bittencourt, A. Metelmann, and G. A. Steele, Generation of large amplitude phonon states in quantum acoustics, Nature Communications 16, 6096 (2025).

• M. Bundgaard-Nielsen, G. L. Lippi, and J. Mørk, Modeling quantum noise in nanolasers using markov chains, Physical Review A 113, 043704 (2026).

• M. Bundgaard-Nielsen, E. V. Denning, M. Saldutti, and J. Mørk, Stochastic approach to the quantum noise of a single-emitter nanolaser, Physical Review Letters 130, 253801 (2023).

•  B. Parvin, Emitted light features of a three-level atom enclosed in an optical cavity, Chinese Journal of Physics 80, 46 (2022).

• W. Ge, K. Jacobs, and M. S. Zubairy, The power of microscopic nonclassical states to amplify the precision of macroscopic optical metrology, npj Quantum Information 9, 5 (2023).

• T. Tiecke, J. D. Thompson, N. P. de Leon, L. Liu, V. Vuleti´c, and M. D. Lukin, Nanophotonic quantum phase switch with a single atom, Nature 508, 241 (2014).

• R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Esteve, and J. Reichel, Cavity-based single atom preparation and high-fidelity hyperfine state readout, Physical review letters 104, 203602 (2010).

• A. Reiserer and G. Rempe, Cavity-based quantum networks with single atoms and optical photons, Reviews of modern physics 87, 1379 (2015).

• H. Walther, B. T. Varcoe, B.-G. Englert, and T. Becker, Cavity quantum electrodynamics, Reports on Progress in Physics 69, 1325 (2006).

• M. Pelton, C. Santori, J. Vuckovi´c, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Efficient source of single photons: a single quantum dot in a micropost microcavity, Physical review letters 89, 233602 (2002).

• H. J. Kimble, Strong interactions of single atoms and photons in cavity qed, Physica Scripta 1998, 127 (1998).

• M. Kiffner, M. S. Zubairy, J. Evers, and C. Keitel, Two-mode single-atom laser as a source of entangled light, Physical Review A—Atomic, Molecular, and Optical Physics 75, 033816 (2007).