Incoherent control of optical signals: Quantum-heat-engine approach

Optical pump-probe signals can be viewed as work done by the matter while transferring the energy between two coherent baths (from pump to probe). In thermodynamics, a heat engine, such as a laser, is a device which performs similar work but operating between two thermal baths. We propose an “incoherent” control procedure for the optical signals using the physics of a quantum heat engine. By combining a coherent laser excitation of an electronic excited state of a molecule with thermal relaxation we introduce an effective thermal bath treating stimulated emission of probe photons as work performed by the heat engine. We optimize power and efficiency for the pump-probe signal using control parameters of the pump laser utilizing a four-level molecular model in the strong and weak coupling regime illustrating its equivalence with the thermodynamic cycle of the heat engine.

Figure 1

(a) Schematic of the pump-probe measurement in molecular system consisting of two electronic states. Pump field resonant with electronic transition $g$-2 excites a vibrational wave packet in the higher energy vibrational state 2, which relaxes to the lower energy vibrational state 1. The probe field then stimulates the emission from state 1 to the excited vibrational level 0 of the ground electronic state. Finally, vibrational relaxation brings the system back to its ground state $g$. (b) Equivalent three-level QHE with transitions between energy levels $g-1$ and $g-0$ driven by hot (at temperature $T_h$) and cold (at $T_c$) heat baths. The single-mode stimulated emission representing the work done by the QHE occurs at $1-0$ transition with the coupling strength $\lambda$.

Figure 2

(a) The population of ground $g$ and lowest excited state 1 obtained using a coherent bath in Eq. (3) (solid lines) and a thermal bath ${\rho }^{th}$ using parameters in Eq. (6) ($--$dashed) and ${\rho }^{\prime th}$ using Eq. (7) ($╶·$dot-dashed). (b) The difference between populations of coherent and thermal baths ${\rho }^c-{\rho }^{th}$ for parameters in Eq. (6). (c) same as (b) but for exact solution of Eq. (1) (${\rho }^{\left(1\right)}$) vs approximate solutions of Eqs. (3) and (7). (d) The time evolution of the microscopic occupation number $n_h\left(t\right)$ in Eq. (6) vs its approximation $n_h^{*}=n_2$ in Eq. (7). The parameters for the simulations are ${\mathrm{\Omega }}_p=0.0001\mathrm{eV}$, ${\mathrm{\Gamma }}_2=0.025{\mathrm{ps}}^{-1}$ and $n_2=1000$.

Figure 3

2D mapping of the efficiency at maximum power ${\eta }^{*}$ in Eq. (11) vs Carnot efficiency ${\eta }_C=1-\tau$. (a) 3D mapping of ${\eta }^{*}$ vs ${\eta }_C$ vs dimensionless pump frequency $c_p$. (b). 2D mapping of the $c_p$ vs ${\eta }_C$ corresponding to (a).

Figure 4

The double sided Feynman-diagram representing the pump-probe signal in Eq. (12). There are a total of six pathways that contribute to the pump-probe signal; diagrams (a)–(c), and their complex conjugate.