Photon blockade via three-body interactions: toward high-purity and bright single-photon sources

This paper proposes a novel photon blockade mechanism driven by three-body interactions between a photonic mode and two qubits, which intrinsically suppresses two-photon states to simultaneously achieve high purity and high brightness, thereby overcoming the fundamental trade-off that limits current single-photon sources.

The Gist

Imagine you are trying to build a machine that releases light particles (photons) one by one, like a vending machine that dispenses exactly one soda can at a time. In the world of quantum computing and communication, having a perfect "single-photon source" is like having the ultimate vending machine. However, building one is incredibly difficult because of a frustrating trade-off:

• The Purity Problem: If you make the machine very strict so it never accidentally drops two cans at once, it becomes so cautious that it barely dispenses anything at all (low brightness).
• The Brightness Problem: If you push the machine to work faster and dispense more cans, it starts making mistakes and occasionally drops two cans together, ruining the "single" quality (low purity).

For years, scientists have been stuck in this loop, unable to have both high speed and high accuracy.

The New Solution: The "Three-Person Handshake"

This paper proposes a brand-new way to build this machine, called Photon Blockade via Three-Body Interactions. Instead of the usual methods, the authors suggest using a specific setup involving one light beam and two "qubits" (tiny quantum switches, like atoms or superconducting circuits).

Here is how it works, using a simple analogy:

The Old Way (Conventional Blockade):
Imagine a narrow hallway where only one person can fit at a time. To stop a second person from entering, you need a very heavy, rigid door (strong coupling) that is hard to build. If the door isn't heavy enough, two people might squeeze through. This is the old method: it requires extreme conditions and is very sensitive to errors.

The Unconventional Way (Interference):
Imagine a hallway with two paths that cancel each other out. If two people try to walk in, their footsteps cancel out, and they can't move. This is the "unconventional" method. However, it's like trying to balance a pencil on its tip; the timing has to be perfect. If the timing is off by a tiny fraction, the cancellation fails, and two people get through. It's also very slow.

The New Way (Three-Body Interaction):
The authors propose a mechanism that acts like a strict bouncer with a unique rule.

1. The Setup: You have a light beam and two qubits (let's call them Qubit A and Qubit B).
2. The First Step: A photon enters and interacts with Qubit B. This is allowed. The system is now in a "one-photon state."
3. The Blockade: Now, imagine a second photon tries to enter. In this new system, the rules of physics change. Because Qubit A is already "busy" or in a specific state, the interaction required to create a second photon simply cannot happen. It's not that the door is heavy or the timing is tricky; it's that the path to the second photon is physically cut off.

Think of it like a dance floor with a specific rule: "You can bring one partner, but if you try to bring a second, the music stops, and the dance floor disappears." The system physically forbids the existence of two photons at once, regardless of how hard you try to push them in.

Why This is a Big Deal

The paper claims this new method solves the old problems in three major ways:

1. No More Trade-off: Because the path to the second photon is completely blocked by the rules of the interaction, you can push the machine to work faster (high brightness) without it ever accidentally spitting out two photons. You get the speed and the purity simultaneously.
2. It's Forgiving: The old methods were like tightrope walking; if you changed the speed or the strength of the push even a little, the whole thing would fail. This new method is like walking on a wide, flat bridge. It works well across a huge range of settings. You don't need "super-strong" connections or "super-weak" pushes; it just works.
3. It's Tough: The system is resistant to "thermal noise" (heat and random jitters). Even if the environment gets a bit messy, the machine keeps producing perfect single photons. Also, unlike the old methods that might flicker or oscillate wildly, this one produces a steady, reliable stream.

The Real-World Application Mentioned

The authors specifically suggest building this using superconducting circuits (the kind used in advanced quantum computers). They propose a setup with two "transmon qubits" and a microwave resonator connected by a special adjustable link.

They calculate that this setup could create a microwave single-photon source that is:

• Extremely Pure: It almost never makes a mistake (less than 1 error in 10,000).
• Very Bright: It can shoot out about 1 million photons per second.

Summary

In short, this paper introduces a new "rule of the game" for quantum light. By using a three-way interaction between light and two quantum switches, they found a way to physically block the creation of a second photon. This allows scientists to finally have a single-photon source that is both fast and perfect, breaking the long-standing barrier that forced them to choose between speed and accuracy.

Technical Summary

Technical Summary: Photon Blockade via Three-Body Interactions

Problem Statement
The generation of high-performance single-photon sources is a fundamental requirement for optical quantum computing, communication, and sensing. The primary mechanism for generating such sources is photon blockade (PB), where the absorption of a single photon prevents the excitation of subsequent photons. However, existing schemes face a critical limitation known as the "purity-brightness trade-off."

• Conventional Photon Blockade (CPB): Relies on strong anharmonicity in the energy spectrum, necessitating strong coupling between optical modes and matter (atoms, quantum dots, superconducting qubits) that significantly exceeds dissipation rates. This restricts CPB to systems with strong nonlinearities.
• Unconventional Photon Blockade (UPB): Utilizes destructive quantum interference to achieve PB in weakly coupled systems. However, it requires exact parameter matching, exhibits a narrow anti-bunching time window (challenging for finite detector resolution), and yields a vanishingly small average photon number ($N$), resulting in extremely low brightness.
• The Trade-off: In both CPB and UPB, attempts to increase brightness by raising the driving strength inevitably degrade the single-photon purity (increasing the second-order correlation function $g^{(2)}(0)$). Consequently, current mechanisms cannot simultaneously achieve high purity and high brightness.

Methodology
The authors propose a novel photon blockade mechanism based on a three-body interaction between a single photonic mode and two qubits. The system is modeled as a hybrid quantum system with the following components:

• Hamiltonian: The system includes a free Hamiltonian for the photon and two qubits, a driving term applied to the second qubit, and a specific three-body interaction term: $\hat{H}_{thr} = J(\hat{a}^\dagger \hat{\sigma}^+_1 \hat{\sigma}^-_2 + \hat{a} \hat{\sigma}^-_1 \hat{\sigma}^+_2)$.
• Mechanism: Under the resonance condition $\omega_2 = \omega_1 + \omega_a$, the three-body interaction couples the states $|n-1, g_1, e_2\rangle$ and $|n, e_1, g_2\rangle$. Crucially, while the system can be excited from the ground state to a single-photon dressed state, the transition path from the single-photon state to the two-photon state is strictly forbidden. This is because the first qubit is already excited in the single-photon subspace, preventing the de-excitation of the second qubit from generating a second photon via the interaction operator $\hat{a}^\dagger \hat{\sigma}^+_1 \hat{\sigma}^-_2$.
• Analysis: The performance is quantified using the steady-state solution of the master equation, analyzing the equal-time second-order correlation function $g^{(2)}(0)$ and the mean photon number $N$. Analytical solutions are derived by truncating the Hilbert space to the two-photon subspace, supported by numerical simulations using the QuTiP package.

Key Contributions and Results
The proposed mechanism, termed Three-Body Photon Blockade (TPB), offers three distinct advantages over CPB and UPB:

1. Broad Parameter Robustness: Unlike CPB, TPB does not rely on spectral anharmonicity and is not restricted by strong coupling requirements. Unlike UPB, it does not depend on exact destructive interference or precise parameter matching. The mechanism operates effectively across a broad parameter space, maintaining strong antibunching even in the weak-coupling regime ($J/\kappa \ll 1$) and under strong driving conditions.
2. Breaking the Purity-Brightness Trade-off: The most significant finding is the ability to simultaneously achieve extreme purity and high brightness.
   • In the weak-coupling regime with optimal detuning ($\Delta=0$), $g^{(2)}(0)$ remains nearly constant (and low, $\approx 10^{-4}$) over a broad range of driving strengths while the mean photon number $N$ increases continuously.
   • The onset of the rise in $g^{(2)}(0)$ and the saturation of $N$ occur in close proximity, allowing for an operating window where both metrics are optimized.
   • This results in an emission rate ($S = \kappa N$) that is orders of magnitude higher than UPB and significantly higher than CPB, while maintaining $g^{(2)}(0)$ values far lower than both.
3. Robustness and Stability:
   • Thermal Noise: TPB maintains strong blockade ($g^{(2)}(0) \approx 10^{-2}$) up to thermal occupation numbers $n_{th} \approx 10^{-5}$, significantly outperforming UPB which degrades at $n_{th} \approx 10^{-9}$.
   • Time-Delayed Correlation: The time-delayed correlation function $g^{(2)}(t)$ exhibits slow variation without the rapid oscillations seen in UPB. This eliminates the need for high detector time resolution to resolve the anti-bunching dip, providing a broad measurement window.

Physical Realization
The authors propose a feasible implementation using a superconducting circuit architecture. The design involves two transmon qubits and a coplanar waveguide resonator coherently coupled via a flux-tunable Josephson coupler. This setup engineers the required three-body interaction while eliminating unwanted two-body couplings. Using realistic parameters (three-body coupling $J/2\pi \approx 10$ MHz and resonator decay $\kappa/2\pi = 100$ MHz), the system is predicted to yield a microwave single-photon source with $g^{(2)}(0) \approx 10^{-4}$ and an emission rate $S \approx 10^6$/s.

Significance
The paper claims that this work provides a fundamental path toward generating high-purity, high-brightness, and robust single-photon sources. By utilizing three-body interactions to intrinsically cut off the excitation path to two-photon states, the mechanism overcomes the longstanding purity-brightness trade-off that has hindered previous PB schemes. The authors assert that this approach is universal, applicable not only to optical photons but also to other bosonic modes such as magnons and phonons, making it a crucial resource for scalable quantum networks and distributed quantum computing.