Nonreciprocal photon bundle emission

This paper demonstrates that directional quantum squeezing in a compound system of coupled optical resonators and a two-level atom enables nonreciprocal, all-optical control of two-photon bundle emission, allowing selective emission from one direction while prohibiting it from the other.

The Gist

Imagine you have a pair of tiny, connected rooms (optical resonators) and a single guest (an atom) who can jump between floors. Usually, if you knock on the door from the left or the right, the guest reacts the same way. But in this paper, the researchers have built a special "one-way mirror" system where knocking from one side makes the guest dance wildly, while knocking from the other side leaves them completely still.

Here is the simple breakdown of how they did it and what happened:

The Setup: A Two-Room House with a Magic Mirror

Think of the system as two whispering-gallery-mode microcavities (let's call them Room A and Room B) connected by a hallway.

• Room A holds our "guest," a two-level atom.
• Room B is special; it's made of a material that acts like a magic mirror when hit by a strong laser.
• The Magic Mirror (Quantum Squeezing): When a strong laser hits Room B from a specific side (Port 3), it creates something called "directional quantum squeezing." In everyday terms, this is like a force that stretches and compresses the space inside the room, but only for light traveling in one direction. It's like a one-way street for light waves.

The Experiment: Knocking on the Doors

The researchers tested what happens when they send a weak "probe" signal (a gentle knock) into the system from two different directions:

1. Knocking from the Left (The "Yes" Side):
When the signal enters from the left, the magic mirror in Room B doesn't interfere. The signal matches the natural rhythm of the system perfectly.

• The Result: The atom and the light in the two rooms start dancing together in a synchronized, energetic rhythm called a "super-Rabi oscillation."
• The Emission: Because of this dance, the system spontaneously spits out two photons (particles of light) at the exact same time. It's like the house has a mechanism that only releases a pair of balloons when you knock from the left.

2. Knocking from the Right (The "No" Side):
When the signal tries to enter from the right, it has to pass through the "squeezed" side of Room B first.

• The Result: The magic mirror changes the rules. It shifts the frequency (the pitch) of the light so that it no longer matches the rhythm of the atom. The "dance" is broken.
• The Emission: Because the rhythm is broken, the system refuses to release the pairs of photons. The "balloon machine" jams.

The Two Types of "Photon Bundles"

The researchers found they could tune the system to create two different types of these "photon bundles" (pairs of light particles) depending on how they set the knobs:

1. Type 1: The pair of photons comes out of Room B (the one with the magic mirror).
2. Type 2: The pair of photons comes out of Room A (the one with the atom).

In both cases, the rule remains the same: The pairs only appear when the signal comes from the "Left." If you try to send the signal from the "Right," the pairs disappear.

Why This Matters (According to the Paper)

The paper claims this is a breakthrough because it combines two difficult concepts:

• Nonreciprocity: Making things work in only one direction (like a diode for light).
• Multiquanta Emission: Creating groups of particles (bundles) rather than just single ones.

By using this "all-optical" approach (using only light and no moving mechanical parts), they created a device that can control exactly when and where these special pairs of light particles are born. The authors suggest this could be useful for building chiral quantum emitters (light sources that only work in one spin direction) and photonic communications that are immune to backscattering (signals that can't be reflected back to cause interference).

In short: They built a light-switch that only turns on a "double-light" bulb when you flip the switch from the left, but stays dark if you flip it from the right, all by using a special laser-induced "squeeze" to change the physics of the room.

Technical Summary

Technical Summary: Nonreciprocal Photon Bundle Emission

Problem Statement
While quantum squeezing is a cornerstone of quantum optics for ultra-precision sensing and nonreciprocal engineering, and multiphoton bundle emission is a critical mechanism for generating multiphoton sources (essential for quantum lithography, communication, and metrology), the intersection of these two fields remains largely unexplored. Specifically, the generation of nonreciprocal multiquanta emission using directional quantum squeezing has not been previously investigated. Existing research has demonstrated nonreciprocal physics and multiphoton emission separately, but a unified framework for directional control of photon bundles via squeezing is lacking.

Methodology
The authors propose a compound system consisting of two coupled whispering-gallery-mode (WGM) optical resonators (cavities $a$ and $b$) and a two-level atom.

• System Configuration: Cavity $b$ is constructed from $\chi^{(2)}$ nonlinear materials and driven by a strong coherent laser field from Port 3. This drive generates a chiral quantum squeezing effect, converting the clockwise (CW) mode of cavity $b$ into a squeezed mode ($b_{cw,s}$) while leaving the counter-clockwise (CCW) mode unsqueezed. Cavity $a$ is coupled to a two-level atom and driven by a weak probe field from either Port 1 (left input) or Port 2 (right input).
• Theoretical Framework: The system is modeled using Hamiltonians in a rotating frame. For the left input, the Hamiltonian ($H_L$) describes standard coupling. For the right input, the Hamiltonian ($H_R$) is transformed via a Bogoliubov transformation to account for the squeezing, resulting in an effective Hamiltonian ($H^s_R$).
• Key Mechanism: The directional quantum squeezing induces an asymmetric frequency detuning and modifies the effective photon hopping interaction strength ($J_s = J \cosh r$) between the resonators depending on the input direction.
• Dynamics Analysis: The study analyzes the system under the Mollow regime (where atomic driving is strong compared to couplings) to identify eigenstates and eigenvalues. The dynamics are governed by a master equation including intrinsic dissipation (photon decay $\kappa$ and atomic decay $\gamma$). Quantum trajectories are simulated using Monte Carlo methods to trace the emission process.

Key Contributions and Results

1. Directional Super-Rabi Oscillations: The study demonstrates that directional quantum squeezing creates a condition where super-Rabi oscillations between specific eigenstates (e.g., $|00+\rangle$ and $|11-\rangle$) occur only when the probe field is input from one direction (left). When input from the opposite direction (right), the modified detuning and coupling break the frequency-matching condition, suppressing these oscillations.
2. Nonreciprocal Two-Photon Bundle Emission: By leveraging intrinsic dissipation, the system achieves two distinct types of nonreciprocal two-photon bundle emission:
   • Type 1 (Cross-Cavity): When the probe enters from the left, the system undergoes super-Rabi oscillations between $|00+\rangle$ and $|11-\rangle$. Dissipation triggers the sequential emission of two photons (one from each cavity) within a short time window, resulting in a two-photon bundle. This is confirmed by a generalized second-order correlation function $g^{(2)}_{2,ab}(0) \ll 1$ (antibunching of pairs) and $g^{(2)}_{1,ab}(0) > 1$. For right-side input, this emission is prohibited, and photon bunching is observed.
   • Type 2 (Single-Cavity): By tuning parameters (specifically the driving parameter $\beta$), a second regime is identified where super-Rabi oscillations occur between $|00+\rangle$ and $|20-\rangle$. This leads to the emission of two photons from cavity $a$ in a bundle, again exhibiting strong nonreciprocity (antibunching for left input, bunching for right input).
3. Statistical Characterization: The nonreciprocal nature is quantified using cross second-order correlation functions ($g^{(2)}_{1}$) and generalized second-order correlation functions ($g^{(2)}_{2}$). The results show "giant nonreciprocity," where the statistical properties of the emitted light (antibunching vs. bunching) are entirely dependent on the input direction.

Significance
The paper claims that this work bridges the fields of nonreciprocal physics, quantum squeezing optics, and multiquanta emission control through an all-optical approach. The primary significance lies in demonstrating that directional quantum squeezing can selectively induce or prohibit multiquanta emission. This enables precise control over entangled photon pairs, ensuring they are generated in specific directions under controlled conditions.

The authors position this strategy as an advancement in nonreciprocal engineering that:

• Operates via an all-optical scheme requiring only single-cavity two-mode matching and eliminating moving parts.
• Utilizes quantum squeezing, a well-established technique, ensuring compatibility with integrated photonic platforms.
• Offers potential applications in chiral quantum emitters and backscattering-immune photonic communications.
• Extends the exploration of all-optical nonreciprocal approaches into the multiquanta physics regime, potentially inspiring further investigations into nonreciprocal quantum superposition, solitons, and sensing.