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E 3

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Lab room: B167 Birge
Lab phone: (510) 643-8152

Photo of atom chip and cavities

E3: Cavity QED on an Atom Chip

By integrating trapped ensembles of ultracold atoms and high-finesse cavities with an atom chip we are able to study and control the classical and quantum interactions between photons and the internal/external degrees of freedom of the atom ensemble.

On this page you can find more information on

Schematic of an atom chip on a silicon substrate incorporating a Fabry Perot cavity. A hole is micromachined in the substrate to allow light in the cavity mode to pass through

The Experiment

Using copper wires embedded in the atom chip we magnetically trap and load an ultracold ensemble of Rb 87 into the cavity.

Cross-Section of chip and cavity. Cavity mirrors are separated by 250 um

We then transfer the ensemble into an optical trap, a very far detuned longitudinal mode of the cavity.

Probe light is coupled to another longitudinal mode and its transmission is recorded exiting the cavity.

Tunable optomechanics

Top Schematic of atom-probe coupling for different well locations. Atoms (grey points) sit at the bottom of the FORT potential (black dashed line). Since the FORT wavelength is incommensurate with that of the probe, different wells lead to different levels of coupling (green dots on blue curve). Bottom Experimentally obtained contrast plot highlighting the atom-probe coupling dependence on the location of the atom cloud.

Our experimental setup, based on a micromachined atom chip, allows us to freely position the atoms relative to the probe standing wave. This enables both linear and quadratic optomechanical coupling. The strength of this coupling, along with the mechanical resonator frequency, can be tuned by varying the intracavity probe field intensity and its detuning from atomic resonance.

Optomechanical resonators generally consist of solid-state devices. Our atom-based resonator does not suffer from many of the drawbacks found in typical solid-state systems, such as significant environmental couplings, thermal occupation of the mechanical resonator mode, and optomechanical parameters fixed during device fabrication.

The ensemble behaves similarly to a dispersive piece of glass, changing the effective length of the cavity.

Top Schematic of a piece of glass inside a cavity. Bottom In our experiments, the trapped ensemble provides the phase shift

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Ponderomotive squeezing

The collective motion of the atoms' center of mass can act to suppress quantum noise fluctuations of the probe light. This suppression is called ponderomotive squeezing.

When the main source of noise on our probe light is photon shot noise, the optomechanical system is dominantly driven by these quantum fluctuations in radiation pressure. In such a system, by detuning our probe light from cavity resonance we close the gain loop and allow the optomechanical response to interfere constructively and destructively with input optical fluctuations, leading to spectral windows of amplification and of sub-shot-noise squeezing.

Power spectral densities of optomechanical response on a full scale (A) and magnified about the region of shot noise (B), in the phase-modulation (PM; red) and amplitude-modulation (AM; blue) quadratures (solid, data; dashed, theory).

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Cavity-aided magnetic resonance imaging

The cavity shift is sensitive to the spin state of the atoms. By applying a large magnetic-field gradient, we can spatially address spins in different lattice sites using radio-frequency (RF) radiation.

By chirping the applied RF, we flip the spins in each lattice site via rapid adiabatic passage. Each flip causes a step in the cavity shift. By taking the derivative of the cavity shift vs. time, we obtain a spatial image of the atom density along the cavity axis.

(A) Cavity shift as a function of time as RF is swept across the magnetic resonances of atoms in neighboring lattice sites. (B) Atom density in the lattice, as extracted from the cavity shift profile. (C) Rapid adiabatic passage with no magnetic-field gradient, showing a 14 kHz Rabi frequency. This is much less than the 50 kHz resonance splitting between adjacent wells, giving us 120 nm spatial imaging resolution.

We can also precisely count atom numbers in single lattice sites. The precision (<10 atoms per site) is small enough to observe sub-Poissonian fluctuations in atom-number differences between sites. To count atom number, we sweep over only one well, measuring the cavity shift for 2.2 ms before and after the sweep.

Atom number counting in a single lattice site. The precision is given by the Allan deviation of the cavity shift measurement. The deviation is large at short measurement times due to shot noise, and is limited by technical noise at long times. At even longer times uncertainty in atom loss is expected to increase the Allan deviation.

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Optical bistability

The intracavity instensity has a nonlinear response to the optomechanical coupling. For large probe photon numbers (relative to the atom trap potential), this leads to optical bistability. This nonlinear response of the light field was experimentally recorded by sweeping over the cavity resonance and observing hysteresis and asymmetry in the transmitted intensity as a function of probe frequency.

Top Theoretically-predicted cavity lineshapes for a large probe potential relative to trap potential. Bottom Recorded cavity transmission for different atom-probe coupling (antinode, linear, node) as a function of detuning from bare cavity resonance. The ratio of probe-to-trap potential is indicated by the variable eta.

Optomechanical frequency shift

The atom-probe coupling modifies the trap in which atoms reside. The overall trap is dependent on the overlap between probe and trap light standing waves (see contrast plot above), and on the atomic motion. The impact atoms have on their potential is captured by a change in the effective frequency of oscillation, termed optomechanical frequency shift. The effective oscillation frequency was experimentally measured by monitoring the amplitude modulation of the transmitted probe light.

Plot of the effective mechanical oscillation frequency of the atoms as a function of well location (same phi as the contrast plot - Fig. 2). The red curve is a single-parameter fit to the data recorded.

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Many-atom cavity QED

Our experiments operate in the dispersive regime of cavity QED, where the atoms remain in the electronic ground state and act as a variable index of refraction inside the cavity.

The cavity resonance is detuned a few gigahertz from the atomic electronic excitation frequency. In this far detuned limit, the dispersive shift from the presence of N atoms shifts the cavity resonance by \Delta_N

In this context we are investigating the optomechanical coupling between photons and the external degrees of freedom of the ensemble, (i.e. the center of mass, the variance, and momentum). In addition we are investigating the coupling of internal spin states (i.e. Zeeman sublevels of F=2 Rb 87) to the cavity photon field.

For more information on cavity QED see relevant sections of the Theses from Kater, Kevin, and Tom

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Chip Construction

Sketch of an atom chip on a sapphire substrate with one mirror of a high finesse cavity directly on the substrate

An atom chip consists of microscopic sized, current carrying wires patterned on some electrically insulating substrate (in our case sapphire or silicon). These wires create magnetic fields which can trap and transport a cloud of cold atoms (in our case 87Rb). We have fabricated atom chips at the UC Berkeley MicroLab, using a copper electroplating process.

The high finesse optical resonator we have chosen to incorporate is a Fabry Perot type optical cavity. At least one of the mirrors forming the cavity is a slightly curved ultralow loss dielectric mirror on the end of a 3mm diameter glass stock. In the case of the sapphire atom chip, the other mirror is laid directly onto the surface of the chip, and patterned into an ~150um diameter pad (just large enough to fit the entire cavity mode spot). For the silicon chips, a hole is machined through the entire substrate via a Deep RIE Bosch type process, and the cavity is finished with another curved mirror, placed underneath the chip. Sketches of the two chips are shown below. For more information on the usefulness of high finesse cavities in atomic physics see the Cavity QED Lab.

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