Abstract
These notes summarize lectures given at the 2019 Les Houches summer school on Quantum Information Machines. They describe and review an application of quantum metrology concepts to searches for ultralight dark matter. In particular, for ultralight dark matter that couples as a weak classical force to a laboratory harmonic oscillator, quantum squeezing benefits experiments in which the mass of the dark matter particle is unknown. This benefit is present even if the oscillatory dark matter signal is much more coherent than the harmonic oscillator that it couples to, as is the case for microwave frequency searches for dark matter axion particles.
Highlights
It is widely accepted from astrophysical observations and the absence of laboratory interactions that dark matter is composed of an as yet unknown fundamental particle with the following properties: it 1.) is weakly interacting, 2.) is ‘cold,’ in that it is non-relativistic and, more strictly, gravitationally bound to our galaxy and to other clusters of galaxies, and 3.) has energy density ρa ≈ 0.4 GeV/cm3 [14, 15]
The second statement is a consequence of the virial theorem and assumes that gravitational interactions have established an equilibrium between ordinary matter and dark matter, implying a Maxwellian velocity distribution for dark matter with a characteristic velocity of v ≈ 300 km/s ≈ c/1000
An apparatus designed to search for such a light particle is quite different than most experiments that search for fundamental particles, where the hypothetical particle is usually much more massive
Summary
It is widely accepted from astrophysical observations and the absence of laboratory interactions that dark matter is composed of an as yet unknown fundamental particle with the following properties: it 1.) is weakly interacting, 2.) is ‘cold,’ in that it is non-relativistic and, more strictly, gravitationally bound to our galaxy and to other clusters of galaxies, and 3.) has energy density ρa ≈ 0.4 GeV/cm3 [14, 15]. The last statement is the value of missing mass density inferred from the visible matter and associated velocity distribution of our local cluster of galaxies These meager facts already have important implications for the quantum statistics of any fundamental, identical particles that would make up dark matter. Experiments that search for this dark matter field often use a “table-top” laboratory apparatus, where the putative coupling of the dark matter causes a parameter in the Hamiltonian of the apparatus to oscillate at the Compton frequency of the dark matter ωa = mac2/ħh This table top apparatus could be a microwave cavity [23], an inductor-capacitor resonant circuit [24], the collective spin of an ensemble of electron or prepare input state evolve under system Hamiltonian measure system statistical inference procedure. The quantum noise in a microwave field is an important limitation in determining whether the halosope cavity evolves under a null hypothesis or if its Hamiltonian has been modified by the dark matter coupling
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