The main part of the talk will be devoted to the results on generation of 8.3dB spin squeezing with this system. The high level of experimental control leads to an almost Heisenberg limited squeezed state which implies strong many particle entanglement. Employing the entanglement witness for the depth of entanglement developed by Sorenson and Molmer one can claim that at least 80 particles out of 400 are entangled within three sigma confidence level. With this massive quantum resource it was possible to demonstrate explicitly the improvement of a Ramsey type matterwave interferometer beyond the classical precision limit. Since the squeezing is realize within the first beamsplitter of the interferometer while the input state is a classical coherent state we refer to this setup as nonlinear matterwave interferometer.
The main part of the talk will be devoted to the results on generation of 8.3dB spin squeezing with this system. The high level of experimental control leads to an almost Heisenberg limited squeezed state which implies strong many particle entanglement. Employing the entanglement witness for the depth of entanglement developed by Sorenson and Molmer one can claim that at least 80 particles out of 400 are entangled within three sigma confidence level. With this massive quantum resource it was possible to demonstrate explicitly the improvement of a Ramsey type matterwave interferometer beyond the classical precision limit. Since the squeezing is realize within the first beamsplitter of the interferometer while the input state is a classical coherent state we refer to this setup as nonlinear matterwave interferometer.
Quantum Sensors, like atom interferometers (AI), can be employed for high-precision measurements of inertial forces, including their application as gravimeters, gradiometers, accelerometers, and gyroscopes. Their measurement principle relies on ultracold atoms that are prepared in quantum-mechanical superposition states in external degrees of freedom. These states can be prepared by a momentum transfer of a Raman laser. Then the superposition state senses the effect of an inertial force, which induce a corresponding relative phase. The phase is read out by a final coupling which converts the interferometric phase into a atom number difference between the two states. The difference provides an estimate of the interferometric phase and the corresponding quantity of interest. The quantum mechanical noise of the atomic ensemble cause a fundamental uncertainty of this estimation, which I analyze for generic AIs. For small atomic densities, the quantum phase noise of the ensemble limits the interferometric sensitivity. For large densities, quantum number fluctuations generate density fluctuations, which generates phase noise. I show that these two competing effects result in an optimal atom number with a maximal interferometer resolution. Squeezed atomic samples allow for a reduction of the quantum noise of one quantity at the expense of an increased noise along of a conjugate quantity. Phase and number are such quantities which obey to a variant of Heisenberg’s uncertainty principle. Neither phase nor number squeezing can improve the maximal interferometer resolution. As one main result of this thesis, I show how an optimal squeezing in between number and phase squeezing, allows for a fundamental improvement. I evaluate possible experimental paths to implement the proposed protocol. Concepts for a squeezing-enhanced operation of external-degree AIs have not yet been demonstrated. I propose and implement an atomic gravimeter, which is designed to accept spin-squeezed atomic states as input states. The interferometer is designed such that the interferometer couplings are performed in spin space, while the phase accumulation is performed in momentum states. For this interferometer, the squeezed input can be directly obtained from spin dynamics in spinor Bose-Einstein condensates. The main noise contributions in the experiment are analyzed, which results in a factor of 84 above the relevant quantum limit, preventing a squeezing enhancement so far. I outline a suppression of the main noise source, uncontrolled AC Stark shift on the squeezed mode and propose future important applications, including test of spontaneous collapse theories and an improvement of large-scale, high-precision gradiometers.
Quantum-enhanced precision measurements have emerged as one of the most useful applications of quantum optics. Exploiting quantum states of light and quantum processes, classical measurement limits can be surpassed, leading to improvements in areas including clocks, spectroscopy, magnetometry, and imaging. One measurement where straightforward quantum enhancements are possible is phase sensing with an interferometer. One can inject squeezed vacuum states into the dark port of the beamsplitter in a traditional interferometer to reduce the quantum noise and reach phase sensitivities beyond the shot noise limit. An alternate approach is to replace the beamsplitters of an interferometer with nonlinear parametric amplifiers, which produce nonclassical states of light that can be used to surpass classical performance. This so called SU(1,1) interferometer can theoretically approach sensitivities that scale as 1/n, the Heisenberg limit where n is the interior phase sensing photon number, compared to the shot noise limit of 1/ √ n for a traditional interferometer [1]. I will present our group’s experimental progress in testing a Mach-Zender SU(1,1) interferometer using four-wave mixers (4WMs) in hot Rb atoms as the parametric beamsplitters. The 4WM process generates entangled twin beams which serve as the two arms of the interferometer, and are then recombined in a second 4WM cell, resulting in a phase-sensitive output. We will extend the work done on this interferometer [2, 3] by performing a detailed analysis of the output signal to noise through homodyne measurements, and will attempt to observe the better-than-shot-noise scaling of the sensitivity. We will also consider the various difficulties of this optical interferometer such as the susceptibility to loss and imperfect mode-matching within the interferometer. Our group is also considering an analogous SU(1,1) interferometer in a cold atom system. Collisions in a spinor Bose-Einstein condensate of sodium atoms give rise to a 4WM process that produces spin states of the atoms which are entangled in atom number. These interactions can be controlled to set up an SU(1,1) atom interferometer, where the relevant measurements are now atomic population differences rather than photon intensities. These enhancements can lead to drastic improvements in atomic spin interferometry [3, 4].
Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as wells as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose-Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
Squeezed states, special kinds of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors, they allow us to overcome the ‘classical’ projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as well as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum-enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial, we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose–Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
The controlled generation of entanglement forms the basis for currently emerging ‘quantum technologies’, such as quantum simulation, computation, and metrology. In the field of quantum metrology, multi-particle entangled states, such as spin-squeezed states, are investigated as a means to improve measurement precision beyond the ‘standard quantum limit’. This limit arises from the quantum noise inherent in measurements on a finite number of uncorrelated particles and limits today’s best atomic clocks. Atom chips combine exquisite coherent control of ultracold atoms with a compact and robust setup, suggesting their use for quantum metrology with portable atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. In this thesis, I present experiments where we generate for the first time multi-particle entanglement on an atom chip. We achieve this by controlling elastic collisional interactions with a state-dependent potential. We employ this novel technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are a useful resource for quantum metrology, as they could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. The state-dependent potential is created with the help of a coplanar microwave guide, which is integrated on our atom chip. In the vicinity of this waveguide a microwave nearfield is formed. When a Bose-Einstein condensate of 87Rb is brought into this near-field, the hyperfine energy levels of the atoms are shifted differentially due to the AC Zeeman effect. The strong gradients in the field can be used to state-selectively shift the minimum of a static magnetic atom trap and thus coherently split an ensemble of atoms which have been prepared in a superposition of two internal states. During this process, nonlinear atomic interactions lead to the formation of a spinsqueezed state. I tomographically analyze the produced state, reconstruct its Wigner function, and deduce that it is at least four-particle entangled. I compare our results with a dynamical multi-mode simulation which takes not only the atomic motion and internal state dynamics but also particle losses into account and find good agreement. Moreover, I use this comparison to identify technical noise sources in our experiment, which currently limit the achieved amount of squeezing, and make suggestions on how to eliminate them in future experiments. Our method can in principle create a very large amount of squeezing and entanglement and is applicable to a wide variety of atomic systems, in particular to those for which no convenient Feshbach resonance exists. We envisage the implementation of this technique in portable atomic clocks and interferometers operating beyond the standard quantum limit. Furthermore, it is a valuable tool for experiments on many-body quantum physics and could enable quantum information processing on atom chips.
The generation of entanglement in atomic systems plays a central topic in the fields of quantum information storage and processing. Moreover, a special category of entangled states of multi-atom ensembles, spin squeezed states, have been proven to lead to considerable improvement in the sensitivity of precision measurements compared to systems involving uncorrelated atoms. A treatment of entanglement in open systems is, however, incomplete without a precise description of the process of decoherence which necessarily accompanies it. The theory of entanglement and decoherence are the two main topics of this thesis. Methods are described for the generation of strong correlations in large atomic ensembles using either cavity quantum electrodynamics or measurement outcome conditioned quantum dynamics. Moreover, the description of loss of entanglement resulting from the coupling to a noise reservoir (electromagnetic vacuum) is explored. A spin squeezing parameter is used throughout this thesis as both a measure of entanglement strength and as an indication of the sensitivity improvement above the so-called standard quantum limit (sensitivity obtained with uncorrelated particles) in metrology. The first scheme considered consists of a single mode cavity field interacting with a collection of atoms for which spin squeezing is produced in both resonant and off-resonant regimes. In the resonant case, transfer of squeezing from a field state to the atoms is analyzed, while in the off-resonant regime squeezing is produced via an effective nonlinear interaction (one-axis twisting Hamiltonian). A second, more experimentally realistic case, is one involving the interaction of free space atoms with laser pulses; a projective measurement of a source field originating from atomic fluctuations provides a means of preparing atomic collective states such as spin squeezed and Schrodinger cat states. A new unravelling is proposed, that employs the detection of photon number in a single output channel and is capable of producing mesoscopic Schrodinger cat states in a single step. As a first step to understanding the role of cooperative decoherence, of importance in the case of dense pencil-shaped atomic ensembles, the collective spin decoherence of a two multilevel atom system is derived. This calculation is also relevant to entanglement loss for two qubits manipulated using with reading/writing pulses. Finally, a scheme is proposed in which arbitrarily strong entanglement can be produced in a four-wave mixing setup, where the preparation of the atoms in a dark state limits the decoherence to negligible values.