Question Bank MCQ • 2 Marks Section 6: Atomic and Molecular Physics Lasers and Quantum Optics

QB_PH_SEC6_017: Lasers and Quantum Optics

Question Statement

Why is a four-level laser system (e.g., Nd:YAG) fundamentally more energy-efficient for achieving population inversion than a three-level laser system (e.g., Ruby)?
(A) The lower laser level in a four-level laser is situated well above the ground state and is rapidly emptied by fast non-radiative decay, maintaining $N_1 \approx 0$
(B) Four-level lasers bypass the requirement for optical pumping entirely
(C) Stimulated emission is strictly forbidden in three-level systems
(D) The spontaneous lifetime of the upper laser state is infinitely long in a four-level laser
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Step-by-Step Derivation & Verification: 1. **Three-Level Dynamics (Ruby)**: - Lasing transition occurs directly to the ground state: $E_2 \to E_1 = E_0$. - Population inversion requires $N_2 > N_1$. - Total atoms $N = N_1 + N_2 \implies N_2 > N/2$. At least $50\%$ of all atoms in the medium must be excited, requiring a very high pump threshold. 2. **Four-Level Dynamics (Nd:YAG)**: - Lasing transition occurs between excited states: $E_2 \to E_1$, where $E_1 > E_0$. - The lower level $E_1$ empties extremely quickly to the ground state $E_0$ via rapid non-radiative relaxation ($E_1 \gg k_B T$). - Thermal population $N_1(0) = N_0 e^{-(E_1 - E_0)/k_B T} \approx 0$. - Any finite number of atoms in $E_2$ satisfies $N_2 > N_1 \approx 0$, dramatically lowering the pump threshold. 3. **Conclusion**: Option (A) is correct.
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