Abstract
Based on concepts from quantum thermodynamics the two-level system coupled to a single electromagnetic mode is analyzed. Focusing on the case of detuning, where the mode frequency does not match the transition frequency, effective energies are derived for the levels and the photon energy. It is shown that these should be used for energy exchange with fermionic and bosonic reservoirs in the steady state in order to achieve a thermodynamically consistent description. While recovering known features such as frequency pulling or Bloch gain, this sheds light on their thermodynamic background and allows for a coherent understanding.
Highlights
Two-level systems are the paradigm for the interaction of matter with light
Detuning is known to have a variety of practical consequences, e.g., it results in frequency pulling [1] for lasers and Bloch gain for intersubband transitions in semiconductor heterostructures [2,3]
Such a setup was recently realized experimentally with high conversion efficiency for microwaves [15]. It is a prototype model system for many important devices such as light emitting diodes (LEDs), semiconductor lasers, or semiconductor solar cells, where the upper and lowers levels correspond to conduction and valence band states, respectively
Summary
Two-level systems are the paradigm for the interaction of matter with light. Typically, one considers light frequencies ω/2π , where the photon energy hω matches the energy difference Eu − El between the upper (index u) and lower (index l) levels. Assuming local couplings [12,13,14] of the two levels with separate reservoirs, the energy balance in the steady state allows us to identify effective energies for the levels and the electromagnetic mode These differ from the bare energies by a fraction of the detuning which is proportional to the contribution to the total broadening, see Eqs. Such a setup was recently realized experimentally with high conversion efficiency for microwaves [15] It is a prototype model system for many important devices such as light emitting diodes (LEDs), semiconductor lasers, or semiconductor solar cells, where the upper and lowers levels correspond to conduction and valence band states, respectively. For these examples, it is shown that the effective energies introduced here provide the same features as detailed microscopic calculations performed before. Appendix C details how the effective energies can be generalized to arbitrary systems with fermionic baths
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