Quantum lithography, entanglement and Heisenberg-limited parameter estimation

  title={Quantum lithography, entanglement and Heisenberg-limited parameter estimation},
  author={Pieter Kok and Samuel L. Braunstein and Jonathan P. Dowling},
  journal={Journal of Optics B-quantum and Semiclassical Optics},
We explore the intimate relationship between quantum lithography, Heisenberg-limited parameter estimation and the rate of dynamical evolution of quantum states. We show how both the enhanced accuracy in measurements and the increased resolution in quantum lithography follow from the use of entanglement. Mathematically, the hyper-resolution of quantum lithography appears naturally in the derivation of Heisenberg-limited parameter estimation. We also review recent experiments offering a proof of… 
Quantum optical metrology – the lowdown on high-N00N states
Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is
Entangled States of Atomic Solitons for Quantum Metrology
Abstract The formation of multiparticle maximally path-entangled states (known as N 00 N -states) are considered along with their use in quantum metrology. It is shown how the standard quantum limit
Quantum Optical Technologies for Metrology, Sensing, and Imaging
Over the past 20 years, bright sources of entangled photons have led to a renaissance in quantum optical interferometry. Optical interferometry has been used to test the foundations of quantum
Nonlinear quantum metrology with moving matter-wave solitons
The estimation of some parameters with super-Heisenberg sensitivity, i.e. beyond Heisenberg limit, is one of the principal problems for current quantum metrology. We propose to use Bose Einstein
Quantum metrology beyond Heisenberg limit with entangled matter wave solitons
It is revealed that the ratio between two-body scattering length and intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.
Entanglement is not a critical resource for quantum metrology
We investigate high-precision measurements beyond the standard quantum limit, utilizing nonclassical states. Although entanglement was considered a resource for achieving the Heisenberg limit in
Parity measurements in quantum optical metrology
We investigate the utility of parity detection to achieve Heisenberg-limited phase estimation for optical interferometry. We consider the parity detection with several input states that have been
Quantum metrology beyond Heisenberg limit with entangled matter wave solitons
Considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic nonclassical states, including
Quantum Optical Metrology, Sensing and Imaging
In this dissertation we begin with a brief introduction to quantum optics concentrating on the topics of the noise of quantum optical states, quantum estimation theory, quantum interferometry and the
The parity operator: Applications in quantum metrology
In this paper, we review the use of parity as a detection observable in quantum metrology as well as introduce some original findings with regards to measurement resolution in Ramsey spectroscopy and


Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit
It is shown how to write arbitrary 2D patterns by using the nonclassical photon-number states method, and a factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion.
Two-photon diffraction and quantum lithography.
Utilizing the entangled nature of a two-photon state, the experimental results have beaten the classical diffraction limit by a factor of 2 and are a quantum mechanical two- photon phenomenon but not a violation of the uncertainty principle.
Entangled-state lithography: tailoring any pattern with a single state.
A systematic approach to Heisenberg-limited lithographic image formation using four-mode reciprocal binomial states by controlling the exposure pattern with a simple bank of birefringent plates, which shows any pixel pattern on a (N+1) x (N-1) grid can be generated from a 2N-photon state.
Quantum-interferometric optical lithography: Towards arbitrary two-dimensional patterns
As demonstrated by Boto et al. [Phys. Rev. Lett. 85, 2733 (2000)], quantum lithography offers an increase in resolution below the diffraction limit. Here, we generalize this procedure in order to
Linear optics and projective measurements alone suffice to create large-photon-number path entanglement
We propose a method for preparing maximal path entanglement with a definite photon-numberN, larger than two, using projective measurements. In contrast with the previously known schemes, our method
Quantum-enhanced positioning and clock synchronization
This work reports that quantum entanglement and squeezing can be employed to overcome the classical limits in procedures such as positioning systems, clock synchronization and ranging and uses frequency-entangled pulses to construct quantum versions of these protocols.
Complementarity and Fundamental Limit in Precision Phase Measurement.
  • Ou
  • Physics
    Physical review letters
  • 1996
It is proved that given the total mean number of available photons, the fundamental limit in precision measurement of a phase shift is the Heisenberg limit, i.e., $1/〈n〉$.
Generation of maximally entangled photonic states with a quantum-optical Fredkin gate
When a quantum-optical Fredkin gate is embedded into a Mach-Zehnder interferometer, state reduction techniques permit the generation of maximally entangled states of the radiation field when Fock
I derive the quantum phase-noise limit to the sensitivity of a Mach-Zehnder interferometer in which the incident quantum particles enter via both input ports. I show that if the incident particles
Conditional generation of N -photon entangled states of light
We propose a scheme for conditional generation of two-mode N-photon path-entangled states of traveling light field. These states may find applications in quantum optical lithography and they may be