Quantum States Show Hidden Correlations Across Distances

A new quantum state created in atomic ensembles reveals strong correlations between distant particles, similar to the famous Einstein-Podolsky-Rosen (EPR) paradox, where measuring one particle instantly affects another. This breakthrough, using a two-axis two-spin squeezed (2A2S) state, allows researchers to study quantum entanglement—a key resource for quantum computing and secure communication—without needing extremely precise single-atom measurements. For everyday readers, this means scientists can now probe the strange connections between particles that Einstein called 'spooky action at a distance' using simpler, more accessible s.

The researchers found that the 2A2S state exhibits squeezing, where quantum noise is reduced in certain combined variables of two atomic ensembles. Specifically, the variances of observables like ~S_x1 + ~S_x2 and ~S_y1 - ~S_y2 drop significantly at optimal times, as shown in Figure 1(a), with values as low as 2N e^{-2Nτ} for short interaction times. This squeezing indicates that the two ensembles are highly correlated, much like two synchronized pendulums swinging in perfect harmony, but at a quantum level where their properties are linked regardless of distance.

To generate this state, the team applied a specialized Hamiltonian—a mathematical description of the system's energy—to two Bose-Einstein condensates (BECs) or atomic ensembles, each containing atoms with two internal states. Starting with all atoms polarized in one direction, they evolved the system over time, creating a superposition of states where particle numbers in the two ensembles are perfectly correlated. This approach builds on s described in the paper, using numerical simulations to track the state's evolution without relying on approximations that break down for longer times. Essentially, they 'twisted' the quantum states in a way that links the ensembles, similar to braiding two ropes together so that pulling one affects the other.

The data shows that entanglement, measured by the von Neumann entropy, reaches nearly maximum levels at optimal times, as depicted in Figure 5(a)-(b), with values approaching log₂(N+1) for large ensemble sizes. For example, with N=20 atoms per ensemble, the entanglement oscillates but remains high, indicating persistent quantum connections. The state also violates a Bell inequality—a test for quantum non-locality—with the Bell-CHSH expression C exceeding 2, as shown in Figure 10(a), scaling roughly as 2 + 0.55/N. This violation diminishes with larger ensembles but is detectable without parity measurements, making it easier to observe in experiments. The probability distributions in Figure 4 reveal that measurements in bases like (~S_x1, ~S_x2) show strong correlations, with peaks when ~S_x1 = -~S_x2, reinforcing the EPR-like behavior.

In practical terms, this research matters because it simplifies the detection of quantum entanglement, which is crucial for developing quantum technologies like secure networks and advanced sensors. For instance, such states could improve gravitational wave detectors or enable more robust quantum cryptography by providing correlated resources that are less sensitive to measurement errors. The ability to generate these states with high fidelity—up to 90% for large N, as seen in Figure 6(b)—means they could be implemented in real-world systems where precise atom counting is challenging.

However, the study has limitations: the oscillations in squeezing and entanglement are aperiodic and not perfectly periodic, as noted in the paper, and the Bell violation weakens with increasing ensemble size. This means that for very large systems, the quantum correlations become harder to detect with current s, and the optimal times for different properties (like squeezing versus entanglement) do not exactly coincide, requiring careful tuning in experiments.