Rydberg Atom

When an atom’s outermost electron is excited to a very high energy level characterized by principal quantum number n, the atom enters a Rydberg state. The properties of Rydberg atoms scale dramatically with n: the orbital radius scales as n^2 (in units of the Bohr radius), the electric dipole moment scales as n^2, the radiative lifetime scales as n^3, and the van der Waals interaction coefficient C_6 between two Rydberg atoms scales as n^11. For typical values used in quantum computing (n = 50-100), these scalings yield orbital sizes of micrometers (comparable to a bacterium), lifetimes of hundreds of microseconds, and interaction energies that are orders of magnitude larger than ground-state van der Waals forces. The large dipole moment is what makes Rydberg atoms useful as mediators of two-qubit interactions: two atoms separated by several micrometers can interact strongly through their Rydberg-state dipole-dipole coupling, even though in their ground states the same atoms would be nearly non-interacting at that distance.

The Rydberg blockade is the mechanism used to implement two-qubit entangling gates in neutral atom quantum computers. When atom A is excited to a Rydberg state |r>, the strong dipole-dipole interaction shifts the energy of the doubly-excited state |r,r> by an amount V(R) = C_6 / R^6, where R is the interatomic separation. If this shift is much larger than the Rabi frequency Omega of the excitation laser (the blockade condition: V >> h*Omega), then the doubly-excited state is no longer resonant with the laser, and two atoms cannot both be excited simultaneously. This is the blockade: if the control atom is in |r>, the target atom cannot be excited. A standard implementation of a controlled-Z gate uses three pulses: a 2-pi pulse on the control atom (which acquires a phase of -1 if it starts in |1> and is excited through the Rydberg state, but does nothing if it starts in |0>), a 2-pi pulse on the target atom (which is blocked if the control is in |r>), and another 2-pi pulse to de-excite the control. The net result is a CZ gate up to local single-qubit phases.

The main decoherence sources for Rydberg qubits are spontaneous emission from the Rydberg state and blackbody radiation. Spontaneous emission limits the coherence to the radiative lifetime of the Rydberg state, typically a few hundred microseconds for n around 70 in alkali atoms (rubidium and cesium are the most commonly used). Blackbody radiation at room temperature has a peak near frequencies that drive transitions between nearby Rydberg levels (n to n+1 or n-1), causing additional decoherence that scales as n^5. This limits practical experiments to n values below about 100 at room temperature; some groups use cryogenic environments to suppress blackbody-induced transitions. Atom loss from the tweezer trap during Rydberg excitation is another concern, since the Rydberg electron’s large orbit can overlap with the trapping laser field in a way that reduces the trapping potential, leading to anti-trapping forces during the gate operation. Magic-wavelength traps and pulsed trapping schemes are active areas of research to suppress this loss.