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INVESTIGATION OF QUANTUM FLUCTUATIONS IN A NONLINEAR INTERFEROMETER WITH HARMONIC GENERATION AND COHERENT INTERACTION OF LIGHT AND CS ATOMS

Prashant Srinivasan

Published Aug 23, 2013• 0 citations
Publisher

Abstract

In the first part of this thesis, we investigate the propagation of quantum fluctuations in a nonlinear interferometer comprising under conditions of harmonic generation by computer simulations. This investigation assumes idealized conditions such as lossless and uniform nonlinear media, an ideal cavity and ideal photodetectors. After linearizing wave equations for harmonic generation with a coherent state input, we obtain equations for one dimensional spatial propagation of the mean field and quantum fluctuations for initial conditions set by arbitrary interferometer phase. We discover that fluctuations are de-squeezed in the X and Y quadratures as the interferometer phase is tuned. However, we discover that there is are quadratures P-Q obtained by rotating the X-Y quadratures for which squeezing is improved by factors of 10^9. We present a practical idea to implement rotation of X quadrature fluctuations to the Q quadrature by using an ideal empty optical cavity. Signal-to-Noise ratio of the nonlinear interferometer was calculated and compared with that of a linear interferometer with coherent state input. We calculated a maximum performance improvement of a factor of 60 for a normalized propagation length ζ0 = 3 under ideal conditions. In the second part of this thesis, we investigate experimentalarrangements to transfer atomic coherence from light to cesium atoms. We discuss the experimental arrangement to generate coherence under conditions of electromagnetically induced transparency (EIT). We measure a continuous wave EIT width of 7.18 MHz and present results for pulsed arrangements.

DOI
10.7912/c2/2423

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In the first part of this thesis, we investigate the propagation of quantum fluctuations in a nonlinear interferometer comprising under conditions of harmonic generation by computer simulations. This investigation assumes idealized conditions such as lossless and uniform nonlinear media, an ideal cavity and ideal photodetectors. After linearizing wave equations for harmonic generation with a coherent state input, we obtain equations for one dimensional spatial propagation of the mean field and quantum fluctuations for initial conditions set by arbitrary interferometer phase. We discover that fluctuations are de-squeezed in the X and Y quadratures as the interferometer phase is tuned. However, we discover that there is are quadratures P-Q obtained by rotating the X-Y quadratures for which squeezing is improved by factors of 10^9. We present a practical idea to implement rotation of X quadrature fluctuations to the Q quadrature by using an ideal empty optical cavity. Signal-to-Noise ratio of the nonlinear interferometer was calculated and compared with that of a linear interferometer with coherent state input. We calculated a maximum performance improvement of a factor of 60 for a normalized propagation length ζ0 = 3 under ideal conditions. In the second part of this thesis, we investigate experimentalarrangements to transfer atomic coherence from light to cesium atoms. We discuss the experimental arrangement to generate coherence under conditions of electromagnetically induced transparency (EIT). We measure a continuous wave EIT width of 7.18 MHz and present results for pulsed arrangements.
Atom interferometer measurements are affected by the amount of quantum noise from the laser used to detect atoms. To improve the quantum limited sensitivity of interferometers, there needs to be a way to reduce the amount of quantum noise. Light is composed of two quadratures, where the product of the noise in each quadrature cannot be below a minimum threshold set by the Heisenberg Uncertainty Principle. However, the noise in one quadrature can be reduced at the expense of the other. This form of light is referred to as “squeezed light.” Squeezed light can be produced using four-wave mixing (FWM). Electromagnetically induced transparency (EIT) is an interference phenomenon that occurs when a three-level atom is driven by a coherent field that makes a non-linear medium transparent to the probing field and holds a great deal of similarities to FWM. This thesis developed a theoretical framework that describes the measurement of atomic states and associated noise when quantum light is used to drive the atom and lays the groundwork to produce squeezed light through developing an experiment to produce EIT, as well as discussing the similarities between EIT and FWM to create and further study FWM for improved atom interferometry.
Optical fibers offer considerable advantages over bulk nonlinear media for the generation of squeezed states. This thesis reports on experimental investigations of reducing quantum noise by means of squeezing in nonlinear fiber optic interferometers. Fibers have low insertion loss which allows for long interaction lengths. High field intensities are easily achieved in the small cores of single mode fibers. Additionally, the nonlinear process employed is self phase modulation or the Kerr effect, whose broad band nature requires no phase matching and can be exploited with ultra-short pulses of high peak intensity. All these advantageous features of fibers result in easily obtained large nonlinear phase shifts and subsequently large squeezing parameters. By the self phase modulation process a correlation is produced between the phase and amplitude fluctuations of the optical field. The attenuated or squeezed quadrature has a lower noise level than the initial level associated with the coherent state field before propagation. The resulting reduced quantum noise quadrature can be utilized to improve the sensitivity of a phase measuring instrument such as an interferometer.
By solving linearized wave equations of nonlinear polarization for a medium, we derive the input-output relationship for the propagation of the quantum fluctuations in single-pass second-harmonic generation with arbitrary interaction length. Spectra of quadrature-phase squeezing are calculated from the input-output relations. It is found that the intensity fluctuations of both harmonic and fundamental fields are squeezed below the vacuum fluctuation level. For large interaction length, an arbitrary amount of squeezing can be achieved for the fundamental field whereas only 50% squeezing is possible for the harmonic field. The bandwidth of squeezing is determined by the phase-matching condition and can be very broad in this case. The possibility of a quantum-nondemolition measurement in the process is discussed. Some interesting features in quantum fluctuations of the fields are presented.
By employing the input-output theory of damped quantum systems developed by Gardiner and Collett,1 we discuss the propagation of nonclassical fields through optical systems containing frequency selective elements such as Fabry-Perot interferometers. Our results are of general applicability and are expressed in terms of the linearized drift and diffusion coefficients of the generalized Fokker-Planck equation describing the intracavity field of the nonlinear source. The two nonclassical effects of photon antibunching and squeezing are treated in detail with reference to the examples of intracavity harmonic conversion and optical bistability. Not surprisingly photon antibunching can be enhanced by the suppression of the coherent part of the spectrum of intensity fluctuations with a narrow bandwidth cavity. However the enhancement is ultimately limited and the antibunching lost altogether as the amplitude of the coherent carrier is reduced to a level comparable to that of the field fluctuations (which are set by the system size). Following the suggestion of Levenson et al., 2 we investigate the use of auxiliary cavities for the control of phase and amplitude in the propagation and detection of squeezed states of light. While for a small degree of squeezing such filter cavities operate in a straightforward fashion, a mixing of field quadratures can occur as the degree of squeezing increases leading to a loss of nonclassical behavior.
Atom interferometers possess great potential as sensitive and stable acceleration and rotation sensors. Currently, the DoD is interested in leveraging atom interferometry research to improve inertial sensors and develop portable, compact devices based on atom interferometers with strategic-grade performance. Typical atom interferometers measure the acceleration or rotation signal with an on-resonance detection laser field, but these laser fields have inherent noise that degrades the signal-to-noise ratio. The laser noise in one quadrature of the field can be reduced below the so-called shot noise limit at the expense of the other quadrature. Fields with this property are called “squeezed fields.” Although lowering the noise in one quadrature increases noise in the other quadrature (due to Heisenberg’s uncertainty principle), the noise in the other quadrature can be made irrelevant by designing a detection scheme that does not use that quadrature. By reducing light-source noise, atom interferometer measurement precision can be increased. This thesis aims to establish the groundwork for creating squeezed light to be used for the detection of atoms in the ground or excited state of the NPS Atom Interferometry Laboratory atom interferometer.
Nonclassical states of light are of increasing interest due to their applications in the emerging field of quantum information processing and communication. Squeezed light is such a state of the electromagnetic field in which the quantum noise properties are altered compared with those of coherent light. Squeezed light and squeezed vacuum states are potentially useful for quantum information protocols as well as optical measurements, where sensitivities can be limited by quantum noise. We experimentally study a source of squeezed vacuum resulting from the interaction of near-resonant light with both cold and hot Rb atoms via the nonlinear polarization self-rotation effect (PSR). We investigate the optimal conditions for noise reduction in the resulting squeezed states, reaching quadrature squeezing levels of up to 2.6 dB below shot noise, as well as observing noise reduction for a broad range of detection frequencies, from tens of kHz to several MHz. We use this source of squeezed vacuum at 795 nm to further study the noise properties of these states and how they are affected by resonant atomic interactions. This includes the use of a squeezed light probe to give a quantum enhancement to an optical magnetometer, as well as studying the propagation of squeezed vacuum in an atomic medium under conditions of electromagnetically induced transparency (EIT). We also investigate the propagation of pulses of quantum squeezed light through a dispersive atomic medium, where we examine the possibilities for quantum noise signals traveling at subluminal and superluminal velocities. The interaction of squeezed light with resonant atomic vapors finds various potential applications in both quantum measurements and continuous variable quantum memories.