Quantum metrology with Rydberg atoms
Sébastien Gleyzes
Laboratoire Kastler Brossel, College de France, CNRS, ENS-PSL Research University, UPMC-Sorbonne Universites, Paris, France
ABSTRACT
Rydberg states correspond to electron wave function localised at a very
large distance from the nucleus. These giant atoms are thus extremely
sensitive to their electromagnetic field environment. It is possible to
prepare state with very large electric dipole to probe the amplitude of the
electric field, or states with very large angular momentum, able to detect
very small magnetic field. As often in quantum metrology experiment, the
limit of the sensitivity is set by the quantum fluctuations associated with
the state of the atom. To reach the ultimate sensitivity set by the law of
quantum mechanics, called the Heisenberg limit, it is necessary to prepare
the atom in a non-classical states, like a Schrödinger cat state.
Our system is a Rydberg atom with a large quantum principal number n ~ 50.
In the presence of a small electric field defining the quantization axis,
the degeneracy between levels with the same n is lifted. The new
eigenstates, called Stark levels, are defined by the magnetic quantum
number m, which remains a good quantum number, and the parabolic quantum
number n1, with 0≤n1≤ ne-|m|-1.
Since m remains a good quantum number, it is possible, using a radio
frequency field with a well-defined sigma+ polarization, to restrict the
evolution of the atom to a subspace of the Stark manifold where the system
behaves like a large spin J = (n – 1)/2, whose frequency is proportional to
the local amplitude of the electric field. We have used this effective spin
to perform a quantum-enabled measurement of the static electric field. We
prepare a Schrödinger cat state of the Rydberg atom, quantum superposition
of two classically distinct wavefunction with very different
polarizability, and observe how the relative phase between the two
components of the quantum superposition provides a very sensitive signal to
measure the variation of the static electric field. We achieve a precision
that exceeds the SQL and approaches the fundamental Heisenberg limit (HL)
in this context. The single-shot sensitivity reaches 0.3 mV/cm for a 200 ns
interaction time, (8 microvolt/cm/√Hz at a 3 kHz repetition rate). This
highly sensitive, non-invasive space- and time-resolved field measurement
extends the realm of electrometric techniques and could have important
applications.
Driving the Rydberg atom with a combination of sigma+ and sigma-
polarization would also open the way to explore the full set of Stark
level, and in particular prepare quantum superposition of state with same
parabolic number but opposite value of m. Such states are very interesting
for magnetic metrology, as they would correspond to microscopic probe with
up to 100 µB magnetic moment, while at the same time being impervious to
electric field noise.
[1] A. Facon, et al, "A sensitive electrometer based on a Rydberg atom in a
Schrödinger-cat state", Nature 535, 262–265 (14 July 2016)