🔬 atomic physics

Macroscopic position-position entanglement by photon recoil in Rydberg atoms

This paper proposes a method to generate macroscopic position-position entanglement between two spatially separated neutral atoms by leveraging Rydberg blockade-induced photon recoil to displace one atom by microns, followed by recapture in optical traps to create a Bell state with separations in the hundred-micron regime.

Original authors: Xiao-Feng Shi

Published 2026-07-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiao-Feng Shi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine two atoms, let's call them Alice and Bob, sitting in separate, invisible cages (optical traps) a few microns apart. In the quantum world, these atoms can be "entangled," meaning their fates are linked no matter how far apart they are. Usually, this link is about their internal "mood" (like being spin-up or spin-down).

This paper proposes a way to link them based on where they are physically located, creating a "macroscopic" entanglement where the distance between their possible locations is large enough to see with a microscope (hundreds of microns).

Here is how the author, Xiao-Feng Shi, suggests doing it, using a simple story:

The Setup: The "Magic" Laser and the "Bouncer"

The Players: We have two atoms. One is the Control (Alice) and the other is the Target (Bob).
The Rule (Rydberg Blockade): There is a special rule in this quantum world: If Alice gets excited to a high-energy "Rydberg" state, she becomes like a giant, invisible bouncer. If she is in this state, she prevents Bob from getting excited, even if he is right next to her. If Alice is not excited, Bob is free to get excited.
The Push (Photon Recoil): When an atom gets excited by a laser, it doesn't just change its energy; it also gets a tiny physical "kick" from the light particle (photon), like a billiard ball being struck. This kick pushes the atom slightly in a specific direction.

The Dance: Creating the Link

The experiment involves a carefully choreographed dance of laser pulses:

The Superposition: First, we put Alice into a "superposition." This means she is simultaneously in two states: State A (calm, ground state) and State B (excited, Rydberg state).
The Conditional Push:
- Scenario 1 (Alice is State B): Because Alice is excited, she acts as the bouncer. Bob cannot get excited. Since Bob doesn't get excited, he doesn't get kicked. He stays exactly where he started.
- Scenario 2 (Alice is State A): Alice is calm and not acting as a bouncer. Bob is free to get excited. We hit him with a laser that excites him and then immediately de-excites him. This two-step process gives Bob a double "kick" (one forward, one backward relative to the laser, but netting a push in one direction). Bob is now pushed a few microns away from his starting spot.
The Result: Because Alice was in a superposition, the universe is now in a superposition of two realities:
- Reality 1: Alice is excited, Bob is here (original spot).
- Reality 2: Alice is calm, Bob is there (pushed spot).

Now, Alice and Bob are entangled by their positions. If you check and find Bob is at the original spot, you instantly know Alice is in the excited state. If you find Bob has moved, you know Alice is calm.

Making it "Macroscopic" (The Big Jump)

The paper notes that a single kick moves the atom only a tiny bit (nanometers). To make the distance "macroscopic" (visible under a microscope, like 3 to 100 microns), the author suggests two tricks:

The "Staircase" Method (Multiple Rabi Cycles): Instead of doing the push once, repeat the laser dance 10 times. Each time, Bob gets a little more push. It's like pushing a swing; one push is small, but ten pushes in a row send it flying. This moves Bob much further away.
The "Lightweight" Method: Use lighter atoms (like Lithium or Helium-3). Just as it's easier to push a ping-pong ball than a bowling ball, a lighter atom moves much faster and further with the same laser kick. Using Helium-3, the author calculates they could push the atom over 100 microns in a very short time.

The Catch: Catching Them Again

Once the atoms have been pushed apart, they are flying through empty space. To make the entanglement useful, we must catch them again. The paper suggests using "optical tweezers" (focused laser beams) to grab the atoms and put them back into cages.

If the atom was pushed, we catch it in a cage at the new location.
If it wasn't pushed, we catch it in the old location.

Because the atoms were caught in a superposition of these two locations, the entanglement remains.

Why This Matters (According to the Paper)

The author claims this creates a deterministic (guaranteed to happen, not just a lucky guess) link between the physical locations of two separate atoms.

The Analogy: Imagine Alice and Bob are on opposite sides of the Earth. If you find Alice in New York, you instantly know Bob is in London. But if you find Alice in Tokyo, you instantly know Bob is in Sydney. This paper shows how to create that kind of "location link" in a lab using atoms and lasers.
Future Use: The paper suggests this could be a new way to build quantum networks, perhaps by transferring this "location link" from atoms to light particles (photons) traveling through fiber optic cables, creating a deterministic link between light beams.

In summary: The paper proposes using the physical "kick" from laser light, controlled by a quantum "bouncer" rule, to push two atoms into a state where their physical locations are mysteriously linked, creating a new type of quantum entanglement that happens over visible distances.

Technical Summary: Macroscopic Position-Position Entanglement by Photon Recoil in Rydberg Atoms

Problem Statement
Quantum entanglement between spatially separate particles is a fundamental manifestation of quantum mechanics, yet it typically resides in the internal states of particles (e.g., spin or hyperfine levels) rather than their external spatial coordinates. While entanglement in external states has been demonstrated in systems like optical superlattices (NOON states) or atomic clouds, these often involve superpositions of a single material object or spatially overlapping motional states. Generating deterministic entanglement between the real-space positions of two distinct, spatially separate neutral atoms, particularly with separations in the macroscopic (micron to sub-millimeter) regime, remains a significant challenge. Existing methods for photon-based position entanglement are often probabilistic. This paper addresses the need for a deterministic protocol to generate such macroscopic position-position entanglement using neutral atoms.

Methodology
The proposed protocol utilizes Rydberg blockade interactions and photon recoil effects in two spatially separate neutral atoms, labeled as "control" ( $c$ ) and "target" ( $t$ ). The atoms are initially trapped in shallow optical tweezers and cooled to their motional ground states.

Initial State Preparation: The system begins with atom $c$ in a superposition of two internal ground states, $|0\rangle$ and $|1\rangle$ (where only $|1\rangle$ can be excited to a Rydberg state), and atom $t$ in state $|1\rangle$ . Both are in spatial wavepackets $|\psi_0\rangle$ with zero expected momentum.
Rydberg Excitation and Blockade:
- Atom $c$ is subjected to a laser pulse inducing a transition to the Rydberg state $|r\rangle$ . Due to the Rydberg blockade, if atom $c$ is in $|r\rangle$ , atom $t$ cannot be excited.
- Atom $t$ is then subjected to a sequence of laser pulses: a $\pi$ -pulse to excite to $|r\rangle$ , followed by a $\pi$ -pulse with a reversed propagation direction to de-excite back to $|1\rangle$ .
- Case A (Atom $c$ in $|1\rangle$ ): The Rydberg blockade is active. Atom $t$ remains in the ground state and receives no net momentum kick.
- Case B (Atom $c$ in $|0\rangle$ ): The blockade is inactive. Atom $t$ undergoes the full excitation-deexcitation cycle. Because the laser propagation direction is reversed for the de-excitation, atom $t$ receives a net momentum kick of $2\hbar k$ (where $k$ is the laser wavevector).
Free Flight and Recapture: After the internal state manipulation, the trap for atom $t$ $t$ is released, allowing it to fly freely for a time $T$ $T$ . Atom $c$ $c$ is either held or also released depending on the specific entanglement variant.
- If atom $t$ received the momentum kick, its center of mass shifts by a distance $\ell \approx (2\hbar k/m)T$ .
- Optical traps are then switched on at two distinct locations: the original position $r_t$ and the shifted position $r_t + \ell$ .
Entanglement Generation: The final state is a superposition where the internal state of atom $c$ is correlated with the spatial position of atom $t$ . Specifically, if $c$ is in $|0\rangle$ , $t$ is found at $r_t + \ell$ ; if $c$ is in $|1\rangle$ , $t$ is found at $r_t$ .

Key Contributions and Results

Deterministic Macroscopic Entanglement: The paper demonstrates a deterministic method to generate a Bell-like state where entanglement exists in the spatial positions of two separate atoms. The separation distance $\ell$ can reach the hundred-micron regime (sub-millimeter), a scale significantly larger than typical atomic wavepacket overlaps.
Quantitative Estimates:
- Using heavy atoms like Rubidium ( $^{87}\text{Rb}$ ) with a two-photon excitation scheme ( $k \approx 21 \, \mu\text{m}^{-1}$ ) and a flight time of $T = 100 \, \mu\text{s}$ , a spatial separation of $\ell \approx 3.1 \, \mu\text{m}$ is achievable with a single Rabi cycle.
- To increase efficiency, the authors propose using multiple Rabi cycles ( $N$ ). For $N=10$ , the drift speed increases, allowing the same spatial separation to be achieved in a shorter flight time ( $T=10 \, \mu\text{s}$ ). However, this introduces errors due to Rydberg-state decay and Doppler dephasing. Numerical simulations indicate that for $N=10$ , the fidelity remains high ( $F \approx 0.95$ ) provided the Rydberg lifetime is sufficient (e.g., $\tau = 80 \, \mu\text{s}$ ).
- Alternatively, using lighter atoms such as metastable Helium-3 ( $^3\text{He}^*$ ) significantly enhances the velocity gain due to lower mass. For $^3\text{He}^*$ , a flight time of $100 \, \mu\text{s}$ yields a separation of $\ell \approx 102 \, \mu\text{m}$ , making macroscopic entanglement highly feasible.
Decoherence Analysis: The study identifies that while the spatial state has a long lifetime (limited by vacuum pressure), the entanglement is limited by the relaxation time ( $T_1$ ) of the internal qubit states. If the internal state relaxes ( $|0\rangle \leftrightarrow |1\rangle$ ), the environment effectively "measures" the position, erasing the entanglement. Doppler effects from atomic velocity and position spread are analyzed as sources of dephasing but are shown to be manageable with proper sampling and experimental parameters.

Significance and Claims
The paper claims to introduce a new dimension to Rydberg-mediated quantum science by realizing position-position entanglement between spatially separate atoms. The significance lies in:

Macroscopic Scale: Achieving entanglement separations in the micron-to-sub-millimeter range, distinct from internal-state entanglement.
Deterministic Nature: Unlike probabilistic photon-based methods, this protocol offers a deterministic generation of exotic position entanglement.
Quantum Networking Applications: The authors suggest that this position entanglement can be transferred to photonic qubits (e.g., via cavity QED), creating deterministic entanglement between photons in optical fibers based on their existence or absence in specific paths. This offers an alternative route for quantum networking compared to stochastic spontaneous emission methods.

The work remains grounded in theoretical proposals and numerical analysis of existing experimental parameters (e.g., Rabi frequencies, trap depths, and Rydberg lifetimes), asserting feasibility without claiming experimental realization in this specific study.