40 research outputs found
Quantum optical realization of arbitrary linear transformations allowing for loss and gain
Unitary transformations are routinely modeled and implemented in the field of
quantum optics. In contrast, nonunitary transformations that can involve loss
and gain require a different approach. In this theory work, we present a
universal method to deal with nonunitary networks. An input to the method is an
arbitrary linear transformation matrix of optical modes that does not need to
adhere to bosonic commutation relations. The method constructs a transformation
that includes the network of interest and accounts for full quantum optical
effects related to loss and gain. Furthermore, through a decomposition in terms
of simple building blocks it provides a step-by-step implementation recipe, in
a manner similar to the decomposition by Reck et al. [Reck et al., Phys. Rev.
Lett. 73, 58 (1994)] but applicable to nonunitary transformations. Applications
of the method include the implementation of positive-operator-valued measures
and the design of probabilistic optical quantum information protocols.Comment: We also provide a MATLAB code for numerically implementing the full
decomposition on GitHub, at
https://github.com/NoraTischler/QuantOpt-linear-transformation-decompositio
On Small Beams with Large Topological Charge
Light beams can carry a discrete, in principle unbounded amount of angular
momentum. Examples of such beams, the Laguerre-Gauss modes, are frequently
expressed as solutions of the paraxial wave equation. There, they are
eigenstates of the orbital angular momentum (OAM) operator. The paraxial
solutions predict that beams with large OAM could be used to resolve
arbitrarily small distances - a dubious situation. Here we show how to solve
that situation by calculating the properties of beams free from the paraxial
approximation. We find the surprising result that indeed one can resolve
smaller distances with larger OAM, although with decreased visibility. If the
visibility is kept constant (for instance at the Rayleigh criterion, the limit
where two points are reasonably distinguishable), larger OAM does not provide
an advantage. The drop in visibility is due to a field in the direction of
propagation, which is neglected within the paraxial limit.Comment: 6 pages, 2 figures; + supplementary informatio
Necessary symmetry conditions for the rotation of light
Two conditions on symmetries are identified as necessary for a linear
scattering system to be able to rotate the linear polarisation of light: Lack
of at least one mirror plane of symmetry and electromagnetic duality symmetry.
Duality symmetry is equivalent to the conservation of the helicity of light in
the same way that rotational symmetry is equivalent to the conservation of
angular momentum. When the system is a solution of a single species of
particles, the lack of at least one mirror plane of symmetry leads to the
familiar requirement of chirality of the individual particle. With respect to
helicity preservation, according to the analytical and numerical evidence
presented in this paper, the solution preserves helicity if and only if the
individual particle itself preserves helicity. However, only in the particular
case of forward scattering the helicity preservation condition on the particle
is relaxed: We show that the random orientation of the molecules endows the
solution with an effective rotational symmetry; at its turn, this leads to
helicity preservation in the forward scattering direction independently of any
property of the particle. This is not the case for a general scattering
direction. These results advance the current understanding of the phenomena of
molecular optical activity and provide insight for the design of polarisation
control devices at the nanoscale.Comment: 17 pages, 3 figure
Interfering trajectories in experimental quantum-enhanced stochastic simulation
Simulations of stochastic processes play an important role in the
quantitative sciences, enabling the characterisation of complex systems. Recent
work has established a quantum advantage in stochastic simulation, leading to
quantum devices that execute a simulation using less memory than possible by
classical means. To realise this advantage it is essential that the memory
register remains coherent, and coherently interacts with the processor,
allowing the simulator to operate over many time steps. Here we report a
multi-time-step experimental simulation of a stochastic process using less
memory than the classical limit. A key feature of the photonic quantum
information processor is that it creates a quantum superposition of all
possible future trajectories that the system can evolve into. This
superposition allows us to introduce, and demonstrate, the idea of comparing
statistical futures of two classical processes via quantum interference. We
demonstrate interference of two 16-dimensional quantum states, representing
statistical futures of our process, with a visibility of 0.96 0.02.Comment: 9 pages, 5 figure
Strong unitary and overlap uncertainty relations: theory and experiment
We derive and experimentally investigate a strong uncertainty relation valid
for any unitary operators, which implies the standard uncertainty relation
as a special case, and which can be written in terms of geometric phases. It is
saturated by every pure state of any -dimensional quantum system, generates
a tight overlap uncertainty relation for the transition probabilities of any
pure states, and gives an upper bound for the out-of-time-order
correlation function. We test these uncertainty relations experimentally for
photonic polarisation qubits, including the minimum uncertainty states of the
overlap uncertainty relation, via interferometric measurements of generalised
geometric phases.Comment: 5 pages of main text, 5 pages of Supplemental Material.
Clarifications added in this updated versio
Conceptual understanding through efficient automated design of quantum optical experiments
Artificial intelligence (AI) is a potentially disruptive tool for physics and science in general. One crucial question is how this technology can contribute at a conceptual level to help acquire new scientific understanding. Scientists have used AI techniques to rediscover previously known concepts. So far, no examples of that kind have been reported that are applied to open problems for getting new scientific concepts and ideas. Here, we present Theseus, an algorithm that can provide new conceptual understanding, and we demonstrate its applications in the field of experimental quantum optics. To do so, we make four crucial contributions. (i) We introduce a graph-based representation of quantum optical experiments that can be interpreted and used algorithmically. (ii) We develop an automated design approach for new quantum experiments, which is orders of magnitude faster than the best previous algorithms at concrete design tasks for experimental configuration. (iii) We solve several crucial open questions in experimental quantum optics which involve practical blueprints of resource states in photonic quantum technology and quantum states and transformations that allow for new foundational quantum experiments. Finally, and most importantly, (iv) the interpretable representation and enormous speed-up allow us to produce solutions that a human scientist can interpret and gain new scientific concepts from outright. We anticipate that Theseus will become an essential tool in quantum optics for developing new experiments and photonic hardware. It can further be generalized to answer open questions and provide new concepts in a large number of other quantum physical questions beyond quantum optical experiments. Theseus is a demonstration of explainable AI (XAI) in physics that shows how AI algorithms can contribute to science on a conceptual level
Scattering in Multilayered Structures: Diffraction from a Nanohole
The spectral expansion of the Green's tensor for a planar multilayered
structure allows us to semi analytically obtain the angular spectrum
representation of the field scattered by an arbitrary dielectric perturbation
present in the structure. In this paper we present a method to find the
expansion coefficients of the scattered field, given that the electric field
inside the perturbation is available. The method uses a complete set of
orthogonal vector wave functions to solve the structure's vector wave equation.
In the two semi-infinite bottom and top media, those vector wave functions
coincide with the plane-wave basis vectors, including both propagating and
evanescent components. The technique is used to obtain the complete angular
spectrum of the field scattered by a nanohole in a metallic film under Gaussian
illumination. We also show how the obtained formalism can easily be extended to
spherically and cylindrically multilayered media. In those cases, the expansion
coefficients would multiply the spherical and cylindrical vector wave
functions.Comment: 9 pages, 5 figure
Measurement and shaping of biphoton spectral wavefunctions
In this work we present a simple method to reconstruct the complex spectral
wavefunction of a biphoton, and hence gain complete information about the
spectral and temporal properties of a photon pair. The technique, which relies
on quantum interference, is applicable to biphoton states produced with a
monochromatic pump when a shift of the pump frequency produces a shift in the
relative frequencies contributing to the biphoton. We demonstrate an example of
such a situation in type-II parametric down-conversion (SPDC) allowing
arbitrary paraxial spatial pump and detection modes. Moreover, our test cases
demonstrate the possibility to shape the spectral wavefunction. This is
achieved by choosing the spatial mode of the pump and of the detection modes,
and takes advantage of spatiotemporal correlations.Comment: Supplementary information also available. Comments and feedback
appreciated. Compared to the previous version, here we have made the
following changes: -corrected a typo in the text between Eq. (11) and (12)
-corrected a typo in the references -added reference