Quantum Physics Foundations: Stimulated Emission, Lasers, and Coherence

Two photon-emission pathways: spontaneous vs stimulated

Consider an atom, ion, molecule, or semiconductor active medium with an electron in an excited energy level. It can return to a lower level by emitting a photon. Quantum physics allows two distinct pathways for that emission:

• Spontaneous emission: the excited state decays on its own. The emitted photon’s direction, emission time, and phase are essentially random (within the constraints of energy and momentum conservation). This randomness is why ordinary lamps produce light that is hard to make interfere cleanly over long distances.
• Stimulated emission: if an incoming photon has the right energy to match the energy gap, it can trigger the excited system to emit a second photon. The key feature is that the emitted photon is a copy of the stimulating photon: same frequency (energy), same direction, same polarization, and a fixed phase relationship. This “photon cloning” (in this specific sense) is the quantum mechanism behind optical amplification.

You can visualize the two processes with a two-level diagram:

Energy ↑        (excited)  E2  ●  ────────────────┐  spontaneous: emits photon randomly (time/phase/direction)  │  stimulated: incoming photon triggers a matched photon  └───────────────→  (lower)    E1  ●  + photon energy hν = E2 − E1

Both processes respect the quantized energy difference: the photon energy must satisfy hν = E2 − E1. What differs is how ordered the emitted light is.

Population inversion: the condition for net amplification

Stimulated emission competes with absorption. If a photon passes through a medium where many particles are in the lower level, that photon is more likely to be absorbed (promoting a particle upward) than to stimulate emission. For amplification, you need the opposite: more particles in the excited level than in the lower level for the relevant transition. This is called population inversion.

Why inversion is necessary (conceptual rate balance)

For a given transition between levels 2 (upper) and 1 (lower):

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• Stimulated emission rate ∝ number in upper level, N2, times photon density.
• Absorption rate ∝ number in lower level, N1, times photon density.

Net gain requires N2 > N1 for that transition. Without inversion, the medium is a net absorber, not an amplifier.

Energy-level diagrams and “pumping” (how inversion is created)

In practice, lasers use 3-level or 4-level schemes because a simple two-level system is hard to invert continuously (the same light that stimulates emission also drives absorption). A conceptual 3-level picture:

Energy ↑  E3  ●  (pump excites here)        | rapid non-radiative decay  E2  ●  (metastable upper laser level)  ← population builds up here        | laser transition emits hν  E1  ●  (lower laser level)

Pumping means supplying energy to move population upward (via electrical current, another light source, chemical reactions, etc.). The design goal is to make the upper laser level long-lived enough (metastable) to accumulate population, while the lower laser level empties quickly, making N2 > N1 achievable.

Practical step-by-step: checking whether a medium can amplify

1. Identify the lasing transition (the two levels that define the photon energy).
2. Ask where the population sits under pumping: does the upper level accumulate?
3. Ensure the lower level is depleted (fast decay out of the lower laser level helps).
4. Verify net gain: if more emitters are in the upper than the lower for that transition, incoming photons at that frequency are more likely to trigger stimulated emission than be absorbed.

Coherence: phase relationships that make laser light special

Coherence describes how predictable the phase of a wave is across time and space. For light, phase coherence means the electric field oscillations maintain a stable relationship:

• Temporal coherence: the phase remains correlated over time. This corresponds to a narrow spread of frequencies (small linewidth) and enables interference even when paths differ in length.
• Spatial coherence: the phase relationship is consistent across the beam’s cross-section. This enables a beam to be tightly focused and to produce high-contrast interference patterns.

Stimulated emission is the microscopic origin of coherence in lasers: because the emitted photon matches the stimulating photon’s phase and direction, the amplification process preferentially builds a field that is phase-aligned. Spontaneous emission still occurs, but the laser’s feedback and gain select and amplify the coherent component.

Why coherence enables interference-based technologies

Interference requires stable phase relationships. If phase wanders randomly, interference fringes wash out. Coherent light supports:

• Stable interference fringes for sensing tiny length changes (displacement, vibration, refractive index changes).
• High directionality (collimated beams) for precise targeting and efficient coupling into optical fibers.
• High spectral purity (narrow linewidth) for frequency-sensitive measurements and communications.

Resonant cavities and feedback (conceptual): modes and round-trip gain

A laser is not just an amplifier; it is an amplifier with feedback. The most common feedback mechanism is a resonant cavity (e.g., two mirrors facing each other). Conceptually:

• Light bounces back and forth through the gain medium.
• Each pass through the inverted medium amplifies the light via stimulated emission.
• Only certain standing-wave patterns fit the cavity boundary conditions; these are the cavity’s modes.

The laser “turns on” when the amplification per round trip exceeds the losses per round trip (losses include imperfect mirrors, scattering, absorption, and output coupling). This is the threshold condition, described qualitatively as:

(gain per round trip) > (loss per round trip)  → sustained oscillation in one or more cavity modes

Spontaneous emission provides a tiny initial field in many frequencies and directions. The cavity and gain act like a filter-plus-amplifier: the modes that experience the highest net gain dominate, and their phase structure is reinforced by repeated round trips.

Wavelength selection: energy gaps meet cavity conditions

Laser wavelength is not arbitrary; it is selected by two constraints that must both be satisfied:

1) Quantum constraint: transition energy

The active medium provides gain near frequencies where stimulated emission is possible, centered around the energy difference of the lasing transition:

hν ≈ Eupper − Elower

Real media have a gain bandwidth (a range of frequencies) due to broadening mechanisms (e.g., interactions, temperature, material disorder). So the medium does not provide gain at exactly one frequency, but over a window.

2) Cavity constraint: resonant modes

The cavity supports discrete resonant frequencies determined by its geometry. For a simple linear cavity of length L, resonances occur when an integer number of half-wavelengths fits in the cavity (conceptually):

m (λ/2) ≈ L  → allowed wavelengths λm

The laser output typically occurs at wavelengths where cavity modes overlap the gain bandwidth and have net round-trip gain above threshold. Additional elements (etalon, diffraction grating, distributed feedback structures) can further narrow the selection to a single mode.

Practical step-by-step: predicting what wavelength a laser will emit

1. Start with the medium: identify the transition (or band-to-band recombination in semiconductors) that sets the approximate photon energy.
2. Convert energy to wavelength: use λ ≈ hc/(Eupper − Elower) as a first estimate.
3. Apply cavity constraints: determine which cavity modes lie within the gain bandwidth.
4. Account for selection elements: if present, they suppress all but a narrow set of modes.

Applied examples tied to the quantum concepts

Barcode scanners: coherent, directional light for reliable reflection reading

A barcode scanner needs a bright, narrow beam that can be focused to a small spot and swept across black/white stripes. Laser diodes provide this because:

• Quantized energy difference in the semiconductor sets the photon energy (color) appropriate for detector sensitivity and surface reflectivity.
• Stimulated emission produces directional amplification, yielding a beam that can be collimated and focused.
• Spatial coherence helps maintain a tight spot over distance, improving contrast between reflected signals from dark vs light bars.

Step-by-step signal idea:

1. Laser emits a narrow beam at a wavelength set by the device’s active region energy gap.
2. Optics focus/sweep the beam across the barcode.
3. White regions reflect more light; black regions reflect less.
4. A photodiode converts reflected intensity variations into an electrical signal for decoding.

Fiber-optic communication: stimulated emission for sources, coherence for coupling and modulation

In fiber links, you want light that couples efficiently into a tiny core and can be modulated at high speed. Lasers are used because:

• Population inversion in a semiconductor laser under electrical pumping creates net gain, turning electrical energy into optical power efficiently.
• Coherence and narrow linewidth reduce dispersion penalties in some systems and enable dense wavelength-division multiplexing (many closely spaced channels).
• Wavelength selection is engineered to match low-loss fiber windows (commonly near 1.3 µm or 1.55 µm), which correspond to designed energy differences in the active region and cavity/feedback structures.

Step-by-step conceptual link budget chain:

1. Drive current pumps carriers into the active region, creating inversion between relevant states.
2. Stimulated emission amplifies a cavity mode, producing a stable output wavelength.
3. The coherent, directional beam couples into the fiber with low loss.
4. Information is encoded by modulating intensity, phase, or frequency; coherence is essential for phase-based formats and coherent detection.

Precision measurement: interferometry and sensing tiny changes via phase

Many precision instruments rely on converting a tiny physical change into a measurable phase shift. Lasers are ideal because their coherence maintains stable interference. Examples include displacement measurement, vibration sensing, and refractive-index sensing.

• Coherence enables high-contrast interference fringes, so small phase shifts produce detectable intensity changes.
• Narrow linewidth improves temporal coherence length, allowing longer path differences without fringe washout.
• Cavity modes and feedback stabilize the oscillation frequency, improving measurement repeatability.

Step-by-step interferometric sensing (conceptual):

1. Split a laser beam into two paths (reference and sensing).
2. The sensing path reflects off or passes through the quantity being measured (a moving mirror, a vibrating surface, a gas cell).
3. Recombine the beams; the relative phase produces constructive/destructive interference.
4. Convert the resulting intensity changes at a photodetector into displacement, vibration amplitude, or index change.