E6: Local Quantum Control of Few- to Many-Body Quantum Systems in an Optical Cavity

Researchers: Jacquelyn Ho, Leon Lu, Zhenjie Yan, Tai Xiang, Nathan Song

Lab room: Campbell LL104
Lab phone: (510) 664-4841

E6 Virtual Lab Tour:

If you missed the virtual poster session, you can have a look at a recent E6 poster here. Feel free to email us with questions! Our email addresses can be found via the People page.

E6 is a new experimental apparatus which has just recently been completed. E6 investigates the dynamics of ultracold quantum gases coupled to a high finesse optical cavity, thus exploring the physics of cavity QED (cQED). By coupling many ultracold atoms to the photonic mode of an optical cavity and achieving local control of the atoms through high resolution optical imaging and addressing E6 will explore the physics of open and closed quantum many body quantum systems, dissipative state preparation, local Hamiltonian engineering, quantum feedback and more.

 cQED is the physics of atoms which are strongly coupled to the electromagnetic mode of an optical resonator. cQED is a wonderful testbed for quantum and atom optics because in the strong coupling limit the atoms and cavity form a closed quantum system which obeys the Jayne’s Cummings Hamiltonian. This is advantageous because in typical situations in nature quantum systems are beset by a variety of sources of decoherence including atomic spontaneous emission which can spoil delicate quantum effects such as quantum entanglement.

On the other hand, cQED systems are not perfectly closed. This is because a tiny fraction of the light within the optical cavities is transmitted through the cavity mirrors on each round trip. From the perspective of the atomic system inside of the cavity this looks like decoherence as that information is “lost” from the closed system. However, it is important to remember that since the cavity light was strongly interacting with the atomic system, information about the quantum system is encoded in the phase, frequency, and amplitude of this light which is leaking out of the cavity.

E6 has learned from the experience of E3, the existing cavity experiment in the ultracold research group, that 1) it is possible to take advantage of the closedness of a cQED system to mediate novel interactions between atoms by leveraging the optical field to which they are all coupled and 2) it is possible to take advantage of the controllable openness of a cQED system to make extremely precise non-destructive and continuous measurements of the mechanical and spin state of the atoms within the cavity by monitoring and processing the light coming out of the cavity.

E6 is expanding the toolbox of cQED by introducing highly localized optical imaging and addressing of the atomic system within the cavity by placing the atoms at the focus of a very high-resolution custom microscope which peers into the vacuum chamber. In E6 we have begun to demonstrate the ability to confine atoms using optical tweezers sent in through this objective as well as the ability to image atoms our atomic cloud through this objective at high resolution. We will use the local imaging and local addressing through the objective to control the position of atoms within the cavity as well as to mediate tunable interactions between spatially separated atoms.

One of the major goals for this experiment is to simultaneously utilize the sensitive measurement of the atomic sample afforded by measuring the light leaking out of the cavity as well as the precise control afforded by the local optical addressing through the microscope objective by closing a real-time dynamical feedback loop between these two systems and using the detected cavity light to modulate the optical addressing. This will allow us to explore the interface between quantum control, quantum measurement and quantum feedback with possible applications for many body dissipitive state preparation and simulation, quantum information processing and quantum error correction.

This flexible apparatus has a lot of exciting science in its future, and our team is seeking new members! Join PhD students Justin and Emma, postdoc Johannes, and undergrads Alec and Aron!

atom scanning probe

As shown in figure-a, we trap single atoms in a tweezer array spanning in the transverse direction around the center of a high-finesse near-concentric optical cavity. Using fluorescence imaging via a high-NA objective, the 1D tweezer array is capable of a 2D spatial resolved scan of the cavity-field-induced Stark shift of the imaging transition.

During the imaging sequence, we take multiple frames of fluorescence image while ramping up the imaging frequency closer to resonance, resulting in an increasing photon scattering rate indicated as the approach curves in figure-b. By sending light into a cavity mode and inducing AC Stark shifts (proportional to local cavity field intensity) on the relavant states we change the imaging detuning, and therefore shift the approach curves (red) to the left with respect to the zero-cavity-field approach curve (blue).

By spanning the tweezer array in the cavity-radial direction and scanning them dynamically in the cavity-axial direction (figure-c), we can readily map out the Gaussian radial profile (figure-d) and the sinusoidal axial profile (figure-d) of the cavity TEM-00 mode, with axial contrast of 56% that corresponds to a spatial resolution of 270nm, well below the optical resolution limitof the fluorescence imaging system itself, demonstrating super-resolution imaging.

Additional information about this can be found here.

Near Concentric Optical Cavity

Our optical cavity consists of two highly curved high reflective mirrors which face each other. The cavity that we have assembled is in a near-concentric geometry meaning that the length of the cavity (about 1 cm) is just less than the sum of the radii of curvature of the two mirrors. This geometry gives us the longest cavity which allows a high degree of transverse optical access for the high resolution imaging system as well as for a variety of other transverse beams. Additionally, this geometry also ensures a very small mode waist ensuring a large cavity QED cooperativity figure of merit for our system. Said differently, if an atom emits a photon it is highly likely for that to be captured on the cavity mirrors and reflected back towards the atom for repeated closed-system interaction between the photon and the atom.

High resolution Imaging and Addressing System

We have built a custom high NA imaging system based around a commercial objective to give us the ability to probe our atomic system locally. This system is and will be used for the following purposes:

• High resolution absorption and fluorescence imaging

• The creation of very tightly focused `microtraps’ which can be used to trap few or single individual atoms. In addition to trapping the position of these traps can be dynamically tuned to allow real-time control of the position of the atoms within the cavity mode

• Local pumping of the atomic sample, for example we will be able to generate local beams which will complete the 3rd leg of a Raman transition involving the cavity probe mode

• Installation of a DMD being tested on the bench will also us to create arbitary optical potentials in the plane of the atoms to allow us to create density and spin profiles within the atomic gas.

Frequency Sweep measurement of vacuum rabi splitting

If the resonance of the optical cavity is far detuned from the Rb D2 electronic transition then the atoms appear as a dispersive medium to the light. The light receives a phase shift proportional to the number of atoms and the strength of the interaction. When the atoms are in the cavity and impart this phase shift to the light it slightly changes the resonance condition for the cavity (because the cavity resonance condition relies on the round trip phase for light bouncing within the cavity). By sweeping the probe across resonance for a cavity with atoms and without atoms we can measure the atomic shift to cavity resonance and from this estimate the vacuum Rabi splitting for a single atom within our cavity. While these results are preliminary our measurement seems consistent with our predicted values for the Rabi splitting.

Optical Transport and Bose-Einstein Condensation