3,432 research outputs found
Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type
We study the valuation of American-type derivatives in the stochastic volatility model of Barndorff-Nielsen and Shephard (2001). We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condition
Liquidity Risk, Price Impacts and the Replication Problem
We extend a linear version of the liquidity risk model of Cetin et al. (2004)
to allow for price impacts. We show that the impact of a market order on prices
depends on the size of the transaction and the level of liquidity. We obtain a
simple characterization of self-financing trading strategies and a sufficient
condition for no arbitrage. We consider a stochastic volatility model in which
the volatility is partly correlated with the liquidity process and show that,
with the use of variance swaps, contingent claims whose payoffs depend on the
value of the asset can be approximately replicated in this setting. The
replicating costs of such payoffs are obtained from the solutions of BSDEs with
quadratic growth and analytical properties of these solutions are investigated
Coherent population trapping of a single nuclear spin under ambient conditions
Coherent control of quantum systems has far-reaching implications in quantum
engineering. In this context, coherent population trapping (CPT) involving dark
resonances has played a prominent role, leading to a wealth of major
applications including laser cooling of atoms and molecules, optical
magnetometry, light storage and highly precise atomic clocks. Extending CPT
methods to individual solid-state quantum systems has been only achieved in
cryogenic environments for electron spin impurities and superconducting
circuits. Here, we demonstrate efficient CPT of a single nuclear spin in a room
temperature solid. To this end, we make use of a three-level system with a
-configuration in the microwave domain, which consists of nuclear spin
states addressed through their hyperfine coupling to the electron spin of a
single nitrogen-vacancy defect in diamond. Dark state pumping requires a
relaxation mechanism which, in atomic systems, is simply provided by
spontaneous emission. In this work, the relaxation process is externally
controlled through incoherent optical pumping and separated in time from
consecutive coherent microwave excitations of the nuclear spin
-system. Such a pumping scheme with controlled relaxation allows us
(i) to monitor the sequential accumulation of population into the dark state
and (ii) to reach a new regime of CPT dynamics for which periodic arrays of
dark resonances can be observed, owing to multiple constructive interferences.
This work offers new prospects for quantum state preparation, information
storage in hybrid quantum systems and metrology.Comment: 13 pages including supplementary information, links to figures
correcte
Coherent population trapping of a single nuclear spin under ambient conditions
Coherent control of quantum systems has far-reaching implications in quantum
engineering. In this context, coherent population trapping (CPT) involving dark
resonances has played a prominent role, leading to a wealth of major
applications including laser cooling of atoms and molecules, optical
magnetometry, light storage and highly precise atomic clocks. Extending CPT
methods to individual solid-state quantum systems has been only achieved in
cryogenic environments for electron spin impurities and superconducting
circuits. Here, we demonstrate efficient CPT of a single nuclear spin in a room
temperature solid. To this end, we make use of a three-level system with a
-configuration in the microwave domain, which consists of nuclear spin
states addressed through their hyperfine coupling to the electron spin of a
single nitrogen-vacancy defect in diamond. Dark state pumping requires a
relaxation mechanism which, in atomic systems, is simply provided by
spontaneous emission. In this work, the relaxation process is externally
controlled through incoherent optical pumping and separated in time from
consecutive coherent microwave excitations of the nuclear spin
-system. Such a pumping scheme with controlled relaxation allows us
(i) to monitor the sequential accumulation of population into the dark state
and (ii) to reach a new regime of CPT dynamics for which periodic arrays of
dark resonances can be observed, owing to multiple constructive interferences.
This work offers new prospects for quantum state preparation, information
storage in hybrid quantum systems and metrology.Comment: 13 pages including supplementary information, links to figures
correcte
Magnetometry with nitrogen-vacancy defects in diamond
The isolated electronic spin system of the Nitrogen-Vacancy (NV) centre in
diamond offers unique possibilities to be employed as a nanoscale sensor for
detection and imaging of weak magnetic fields. Magnetic imaging with nanometric
resolution and field detection capabilities in the nanotesla range are enabled
by the atomic-size and exceptionally long spin-coherence times of this
naturally occurring defect. The exciting perspectives that ensue from these
characteristics have triggered vivid experimental activities in the emerging
field of "NV magnetometry". It is the purpose of this article to review the
recent progress in high-sensitivity nanoscale NV magnetometry, generate an
overview of the most pertinent results of the last years and highlight
perspectives for future developments. We will present the physical principles
that allow for magnetic field detection with NV centres and discuss first
applications of NV magnetometers that have been demonstrated in the context of
nano magnetism, mesoscopic physics and the life sciences.Comment: Review article, 28 pages, 16 figure
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