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According to several quantum gravity theories there is an effective minimal length beyond which space cannot be probed, possibly the Planck length. It has been suggested that this fundamental limit implies a generalised uncertainty principle (GUP) and corresponding modification of the canonical position-momentum commutation relations. Some of these modified relations are also consistent with general principles that may be supposed of any physical theory. Here we study the noisy behaviour of an optomechanical system assuming a certain commonly studied modified commutator. From recent observations of radiation pressure noise in tabletop optomechanical experiments as well as the position noise spectrum of Advanced LIGO we derive bounds on the modified commutator, which may be used to constrain the minimal length. We find how such experiments can be adjusted to provide significant improvements in such bounds, potentially surpassing those from sub-atomic measurements.
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Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations which are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min- and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min-entropy is exactly one bit.
We analyze general uncertainty relations and we show that there can exist such pairs of non--commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $Delta A$ and $Delta B$ calculated for these vectors is zero: $Delta A,cdot,Delta B geq 0$. We show also that for some pairs of non--commuting observables the sets of vectors for which $Delta A,cdot,Delta B geq 0$ can be complete (total). The Heisenberg, $Delta t ,cdot, Delta E geq hbar/2$, and Mandelstam--Tamm (MT), $ tau_{A},cdot ,Delta E geq hbar/2$, time--energy uncertainty relations ($tau_{A}$ is the characteristic time for the observable $A$) are analyzed too. We show that the interpretation $tau_{A} = infty$ for eigenvectors of a Hamiltonian $H$ does not follow from the rigorous analysis of MT relation. We show also that contrary to the position--momentum uncertainty relation, the validity of the MT relation is limited: It does not hold on complete sets of eigenvectors of $A$ and $H$.
Inflation is an early period of accelerated cosmic expansion, thought to be sourced by high energy physics. A key task today is to use the influx of increasingly precise observational data to constrain the plethora of inflationary models suggested by fundamental theories of interactions. This requires a robust theoretical framework for quantifying the predictions of such models; helping to develop such a framework is the aim of this thesis. We provide the first complete quantization of subhorizon perturbations for the well-motivated class of multi-field inflationary models with a non-trivial field metric, which we show may yield interesting signatures in the bispectrum of the Cosmic Microwave Background (CMB). The subsequent evolution of perturbations in the superhorizon epoch is then considered, via a covariant extension of the transport formalism. To develop intuition about the relationship between inflationary dynamics and the evolution of cosmic observables, we investigate analytic approximations of superhorizon perturbation evolution. The validity of these analytic results is contingent on reaching a state of adiabaticity which we discuss and illustrate in depth. We then apply our analytic methods to elucidate the types of inflationary dynamics that lead to an enhanced CMB non-Gaussianity, both in its bispectrum and trispectrum. In addition to deriving a number of new simple relations between the non-Gaussianity parameters, we explain dynamically how and why different shapes of inflationary potential lead to particular observational signatures. Candidate theories of high energy physics such as low energy effective string theory also motivate single-field modifications to the Einstein-Hilbert action. We show how a range of such corrections allow for consistency of single-field chaotic inflationary models that are otherwise in tension with observational data.
Discussion of physical realization of coordinates demonstrates that the quantum theory of gravity (still absent) should be non-local and, probably, non-commutative as well.
The contrast of an image can be degraded by the presence of background light and sensor noise. To overcome this degradation, quantum illumination protocols have been theorised (Science 321 (2008), Physics Review Letters 101 (2008)) that exploit the spatial correlations between photon-pairs. Here we demonstrate the first full-field imaging system using quantum illumination, by an enhanced detection protocol. With our current technology we achieve a rejection of background and stray light of order 5 and also report an image contrast improvement up to a factor of 5.5, which is resilient to both environmental noise and transmission losses. The quantum illumination protocol differs from usual quantum schemes in that the advantage is maintained even in the presence of noise and loss. Our approach may enable laboratory-based quantum imaging to be applied to real-world applications where the suppression of background light and noise is important, such as imaging under low-photon flux and quantum LIDAR.
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