Generation of squeezed vacuum in atomic ensembles
Any electromagnetic signal is subject to the laws of quantum
mechanics. This means that due to the Heisenberg uncertainty principle, any
optical measurement will have on top of it, noise due to quantum fluctuations,
even if you are measuring the vacuum itself. This limits many measurements to
having a minimum non-zero noise, called shot noise, or the standard quantum
Squeezed light finds applications in precision measurements
as well as optical communications where the signal to noise needs to be as low
as possible. Due to it's special quantum nature, squeezing may also be applied
in other related areas of quantum optics and quantum information.
In our experiment,
we send linearly polarized laser light, made slightly elliptical by vacuum
fluctuations of the horizontal polarization, through a glass cell containing
hot 87Rb atoms. This leads to polarization self-rotation as the light
propagates, resulting in a squeezed vacuum state of the horizontal polarization
at the output of the cell. By mixing this squeezed vacuum field with a strong
local oscillator field in a homodyne detection arrangement and sweeping the
phase between these fields, we can measure the quadrature fluctuations of the
squeezed vacuum. Depending on experimental parameters, we have observed
squeezing at several laser frequencies near the Rubidium atomic transitions
with our highest level of squeezing to date being about 2 dB of noise
Spatial Correlation of Squeezed Quantum Noise
While many experimentally measured characteristics of vacuum squeezing, based on polarization self-rotation in resonant atomic vapor are well described by the existing theory and numerical calculations, there is still a large unpredicted excess noise at higher atomic densities. One possible explanation is a distortion of the squeezing and/or pump field transverse profiles, since it deteriorate the mode matching between the squeezed vacuum field and the local oscillator (pump field).
Superluminal squeezing propagation
Classically, an electromagnetic wave
can be described with an amplitude and a phase, but on the quantum level it is
a flux of photons. This makes it subject to quantum fluctuations –
uncertainties in the amplitude and the phase. A typical laboratory laser will
produce a beam, which can be closely described as a coherent state of light, a
state with minimum uncertainty. Any measurement done on a coherent state will
exhibit this minimum uncertainty by having so called shot noise. There are a
lot of measurements, where it is the limiting factor. But luckily there is a
way to reduce the noise below the shot noise limit.
The experimental setup is shown on
Fig. 1. The squeezed vacuum field is generated by shining a horizontally
polarized laser beam with the wavelength of 795 nm into a glass cell, containing
resonant Rubidium atoms. This laser beam is called pump. Because of the
non-linear nature of the squeezing process, we focus the beam using lens L1 to
make a more intense beam inside the squeezing cell. The beam is collimated back
using lens L2. Under the right conditions the coherent vacuum in the vertical
polarization becomes squeezed, and we are able to manipulate its group velocity
in the second cell called interaction cell in Fig. 1. The strong horizontally
polarized pump creates conditions for Faraday rotation in the second cell and
for certain pump powers vertically polarized squeezed vacuum field experiences
anomalous dispersion that leads to superluminal group velocities. We are able
to bypass the interaction cell using two mirrors to determine the reference vg=c . We then detect the squeezed vacuum
using a homodyne detector . The signal is fed into a spectrum analyzer and
recorded on a digital oscilloscope.
In order to determine the group velocity we modulate the level of squeezing by applying a small magnetic field to the squeezing cell . This degrades the conditions for squeezing generation and leads to modulation show in Fig. 2. The modulation frequency was 3 kHz. We then fit the traces and determine the relative phase between the bypass channel and the interaction channel. This gives us the possibility to calculate the time difference Δ T between the signals arrival time. Values that are bigger than zero indicate a delay, while values that are less than zero indicate advancement. Our result for different pump powers is presented in Fig. 3.
In conclusion, we have experimentally demonstrated that it is possible to observe superluminal squeezed vacuum propagation. The largest measured advancement was 3 μs.
Spectral quantum noise filtering with EIT
The frequency-dependent transmission properties of an EIT medium can be used to manipulate to noise characteristics of a squeezed vacuum or squeezed light state. In Figure 4, we show an example of an EIT transmission window acting as a low-pass filter for the amplitude of squeezed and antisqueezed noise. Outside of the EIT resonance window, the squeezed vacuum photons are absorbed and so the noise amplitudes are filtered, becoming frequency-dependent. We have studied several such interactions of squeezed states of light with resonant atomic media to see how the quantum noise can be influenced. These studies are important to the implementation of squeezed states in quantum memory and quantum information protocols using resonant atoms.