It has been quite some time since your regularly scheduled QCJC posts, but they shall persist! Now, instead of having chosen this article myself, I wanted to present an article that we discussed in the RSL journal club presentation, in the vain hope that having gone to an actual journal club with actual graduate students, my understanding of the paper would have increased slightly. Not convinced? Neither am I.
A bit of background – Jameson mentioned that trapped ion architecture in this post, and there are indeed a number of different architectures beyond the superconducting ones that I tend to be fond of. One of these use trapped neutral atoms for quantum computation. The primary difference between trapped ions and trapped atoms is, obviously, that trapped atoms have no charge. Therefore, it is easier to put trapped atoms in a cavity and not have spurious electromagnetic effects. However, why would you want to put atoms in a cavity in the first place?
The primary crux of this paper is that the authors were able to achieve the entanglement of a stationary qubit (the trapped atom-in-a-cavity qubit with different energy states) with a flying qubit (a photonic qubit with spin), creating a cat state in the process. This process is governed by a photon passing through a cavity and being at a frequency that may or may not be resonant with the cavity. If the photon is on resonance with the cavity, it would gain a phase shift for its spin, and emerge with an extra of phase. The cavities resonance can be affected by the energy state of the trapped atom inside the cavity – when the atom is in an excited energy state, the cavity resonant frequency will be different.
The goal of these researchers was to create a “cat state”, or a state that is superimposed between a |1> and a |0> state. These states have been studied extensively and well characterized, and have been shown to be especially interesting for creating good phase-error tolerant codes. That means that we are looking towards scalable computers, the fundamental logical qubit may one day have lots of these cat states living inside it. For this trapped atom architecture, the cat state was achieved by placing the trapped atom in a very high quality-factor cavity (Q = 6E5), and allowing it to interact. Only when the Rubidium atom was in its ground state would the cavity be off-resonant from the incoming photon. Therefore, if the atom was in a superposition of its ground and excited states, the incoming photon would also pick up a cat state. Typically, these states can either be referred to as even or odd cat states, which makes more sense in the microwave region (where even and odd just refer to the number of photons in the cavity).
Afterwards, all one needs to do is to make a measurement of the photon. As this is primarily a trapped atom lab, they use some interesting Acousto-optical modulators/deflectors to make sure that the signal input lines are clean. The photon eventually ends up in a homodyne detector setup, as a Fabry-Perot detector. Interestingly, the amount of noise contributed by this detection mechanism seem very low, at only 6% total for the detection circuit. The total loss, which primarily comes from loss in the cavity and coherence-reducing effects, comes out to 46%, which is below the threshold of 50% needed to see some interesting effects.
I thought it was interesting how these different quantum properties – energy levels for the atom, and spin states for the photon – were able to be mixed together. Of course, the interaction that governs this is difficult to engineer, but on paper, the Hamilton looks straight-forwards, like any other Jaynes-Cummings Hamiltonian or any other mixing Hamiltonian in general.
Afterwards, the paper goes on to measure the Wigner functions of the photon, in order to demonstrate the cat states of the quantum system. I really need to carefully analyze exactly what Wigner functions are, as they are used quite often for this purpose in this field! One of the interesting side-discussions that the graduate students had was on the presence of a clearly identifiable negative region in the Wigner functions in Fig 1.a, which seemed to be contrary to their expectation. What this actually means is a mystery to me!
Finally, the paper goes on to propose how this could be used as some kind of quantum gate, where the state of the atom would affect the state of the photon. However, the actual effect of a quantum gate does not seem to be demonstrated clearly in the body of this paper, as instead of controlling the atom, they are passively making measurements to show that the logic table of the two systems is analogous to what would happen in a two-qubit gate.
It’s an interesting look at a different quantum computing architecture, one that many groups are still pursuing! Still not as many as those who are pursuing circuit QED, as I hope I will have the chance to do so soon…