Quantum metrology: a sensor network to surpass the standard limit

A collaboration between the LKB and the University of Basel has just reached a key milestone in multiparameter quantum metrology. By splitting a Bose–Einstein condensate into several correlated atomic clouds, the researchers succeeded in jointly measuring several physical parameters with a precision exceeding the standard quantum limit [1].

Many quantum sensors, such as atomic clocks and atomic magnetometers, exploit the phase shift that develops between two energy levels of a system, an atom for example, initially prepared in a superposition of these two levels. Two-level systems can be viewed as spin 1/2 particles, and the phase shift manifests itself as a precession of the spins in the equatorial plane of an imaginary sphere known as the Bloch sphere.

A sensor made of N atoms prepared in the same initial state is described by a “collective spin” of size N/2, whose precession frequency is typically proportional to the physical parameter to be measured. Although these sensors enable some of the most precise measurements in physics, they are intrinsically subject to quantum projection noise, which sets a lower bound on the statistical error of the measurement (the standard quantum limit) in the case of independent atoms.

In a Bose–Einstein condensate of cold atoms with two internal states, interactions provide a nonlinearity that creates correlations between the atoms. The quantum fluctuations of the collective spin describing the internal degrees of freedom of the system are then modified, allowing the precession frequency to be measured with a precision better than the standard quantum limit. These so-called spin-squeezed states have already been realized in the laboratory, and their usefulness for measuring a physical parameter such as the energy difference between two atomic levels has been experimentally demonstrated.

In some situations, however, such as the characterization of a spatially inhomogeneous field, one wishes to determine jointly not one but several unknown physical parameters, corresponding for instance to the different local values taken by the field. By exploiting the idea of spin squeezed states, one can then hope to use a network of correlated sensors (collective spins) to go below the standard quantum limit.

This is precisely what a collaboration between an experimental group at the University of Basel and theoretical researchers at the LKB has demonstrated for the first time using cold atoms. This falls within the field of multiparameter quantum metrology, a rapidly growing area of research.

The network of correlated sensors is obtained by splitting a Bose–Einstein condensate, initially prepared in a spin squeezed state, into several spatially separated components, two or three in practice. Each component forms a collective spin that serves as a sensor, and the parameters to be measured are encoded in the form of a rotation angle of this spin (see figure). In the two parameter case, a 33% reduction in quantum noise (standard deviation of the estimators) was achieved.

In practice, different independent linear combinations of the parameters are measured with quantum enhancement, which requires modifying the quantum correlations of the initial spin-squeezed state. The researchers proposed a protocol based on this principle and demonstrated its optimality for the available resources (a fixed number of atoms and realizations of the initial spin squeezed state).

Small networks of correlated sensors, such as those demonstrated in this work, could be used for local characterization (measurement of the gradient, curvature, or other spatial moments) of an electromagnetic, gravitational, or inertial field, a direction we plan to explore in the future.

[1] « Multiparameter estimation with an array of entangled atomic sensors » Yifan Li, Lex Joosten, Youcef Baamara, Paolo Colciaghi, Alice Sinatra, Philipp Treutlein, Tilman Zibold, Science 2026.

Référence : Yifan Li, Lex Joosten, Youcef Baamara, Paolo Colciaghi, Alice Sinatra, Philipp Treutlein, Tilman Zibold, “Multiparameter estimation with an array of entangled atomic sensors,” Science, 22 Jan 2026, Vol. 391, Issue 6783, pp. 374–378.

https://www.science.org/doi/10.1126/science.adt2442