the dipole blockade

What do we study?

Rydberg atoms are atoms in which one or more of the atom's electrons have been excited into very high energy states. Because the Rydberg electron is so far from the core of the atom, the atom develops exaggerated properties, such as hugh polarizabilities that scale like n7, where n is the principle quantum number. These exaggerated properties lead to strong, tunable interactions among the atoms, which have applications in many different fields of physics.

One of the most important consequences of the strong interactions between Rydberg atoms is the Rydberg excitation blockade, which results from the interactions shifting the energy levels of the atoms. As shown in the figure above, the energy levels deviate from an equidistant ladder. If the shift of the second excited state is great enough such that the excitation laser is out of resonance with the state, then all excitation above the first excitated state is blockaded.

Some of the applications of the Rydberg excitation blockade include quantum computation, quantum cryptography, improved spectroscopic resolution, and atomic clocks. The first proposal to use the blockade for quantum information was in 2000, when Jaksch et. al. suggested a method of generating a fast phase gate (Phys. Rev. Lett. 85, 2208 (2000)) using Rydberg atoms. The motivation discusses this proposal.

As we move toward the goal of quantum computing with Rydberg atoms, we have conducted many interesting studies. We highlight work done converning the Autler-Townes effect with 85Rb. By taking advantage of the long lifetimes of Rydberg atoms (10's of microseconds), and hence small spectroscopic linewidths of Rydberg states, we are able to achieve Autler-Townes spectra with high resolution. These measurements provide a foundation for all later work, as Autler-Townes spectroscopy is a tool for measuring Rabi frequencies with high accuracy.

We have also conducted a spectroscopic measurement of the energy shifts of the second excited state of the Rydberg excitation ladder in different interaction regimes. By applying two sets of excitation pulses with variable frequency (a set because the excitation to Rydberg states is a two-photon excitation), we have measured the lineshape of the 1R - 2R transition. This study is the first spectroscopic proof of the functionality of the Rydberg excitation blockade.

One way of measuring the effectiveness of the Rydberg excitation blockade is to use counting statistics. We have used this method for a range of nD5/2 Rubidium Rydberg states. Counting statistics measurements are particularly useful for measuring blockade effectiveness in small atomic samples and for a variety of different experimental parameters such as excitation Rabi frequencies, detuning, and quantum state.

 

Forces between atoms

All atoms have repulsive or attractive forces between them due to temporary dipole moments, when the electrons of an atom leave the positively charged nucleus unshielded. Typically the positively charged nucleus polarizes (induces a dipole) in nearby atoms causing a temporary dipole-dipole interaction. These temporary off-resonant dipole-dipole interactions are typically named "van der Waals" or "London" forces. Two atoms or molecules with permanent dipole moments, e.g. HCl, interact via on-resonant "dipole-dipole" interactions. These permanent dipole-dipole interactions however are always in addition to van der Waals (temporary dipole-dipole) interactions. The similarity between dipole-dipole and van der Waals interactions is often clouded by the naming convention. They are both calculated using the standard interaction potential of two interacting dipoles. Van der Waals are off-resonant, temporary, second-order interactions, and dipole-dipole interactions are on-resonant, permanent, first-order interactions.

Interatomic van der Waals interactions are present in all matter, and play a large role in determining the melting points of all elements. For example, consider the melting point of He, 4K (-269C), as compared to the melting temperature of Radon at 221K (-52C). In general symmetric atoms like He and Radon must first be cooled down significantly in order to condense, because they cannot align themselves into an array of aligned dipoles as effectively as elliptically shaped atoms. Atoms with more electrons like Radon have larger van der Waals interactions, and thus must be heated more to break the van der Waals bonds and become a gas. This is because the electrons have larger orbits away from the nucleus, leaving the nucleus unexposed with a higher probability. Furthermore, the nucleus of heavier atoms will induce larger dipoles in nearby atoms, and hence larger van der Waals interactions.

 

Interaction Regimes

As briefly mentioned above, there are two interaction regimes for the forces between atoms: the van der Waals regime, and the dipole-dipole regime. We can see how the two regime arise by looking at the Hamiltonian for two particle interactions, shown on the right. Generically, the Hamiltonian contains energies on the diagonal and coupling terms on the off-diagonal. Here, we have a two particle state AA that is coupled to another two particle state BC through an interaction term Vint, and an energy detuning of D. In our case, the interaction term Vint, is the dipole interaction operator. The scaling of this operator is n4/R3.

In the regime of van der Waals interactions, the coupling between the atoms is much less than the energy detuning, D, of the interaction. This leads to energy eigenstates that are shifted in energy by (Vint)2/D. Since D scales like 1/n3, the total scaling of the shift is n11/R6.

Conversely, for dipole-dipole interactions, the energy detuning D is much smaller than the interaction Vint. In this case, the scaling is simply n4/R3.