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High Resolution non-Markovianity in NMR

View Article: PubMed Central - PubMed

ABSTRACT

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

No MeSH data available.


Parameter τ2 has a relation to the correlation parameter q.The values used in the experiment are presented here.
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f7: Parameter τ2 has a relation to the correlation parameter q.The values used in the experiment are presented here.

Mentions: For the experiment, the values of η were very small and this created a huge source of errors in the operations, since they had to be performed in tiny steps and, therefore, were not so different. In fact, the rotations angles were so small that the controlled operations, which simulate the collisions, were very hard to be performed properly. In order to achieve the necessary precision in the experiment the rotations of θ had to be precisely adjusted for each value of η of the specific collision. For adjusting the angles values, two parameters may be varied, the amplitude and duration of the radio frequency pulses. However, varying these two parameters the sequence of operations needed for the corrections changes as well. Therefore, the correct pulse sequences were determined by combining the two analysis and testing in the spectrometer. A good precision could be achieved then and the small rotations, of the order of 0.30 degrees, could be implemented. For the state preparation the pulse sequence shown in Fig. 6 was performed, for more details see refs 36 and 37. The time τ2 of the free evolution here is related to the correlation parameter q as it is presented in Fig. 7. A the end of the circuit a magnetic field gradient in the z-direction is applied, which works as a transversal relaxation time killing the off-diagonal terms of the density matrix of system and environment. Finally, after each run, full state tomography was performed in the state of the system34.


High Resolution non-Markovianity in NMR
Parameter τ2 has a relation to the correlation parameter q.The values used in the experiment are presented here.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037399&req=5

f7: Parameter τ2 has a relation to the correlation parameter q.The values used in the experiment are presented here.
Mentions: For the experiment, the values of η were very small and this created a huge source of errors in the operations, since they had to be performed in tiny steps and, therefore, were not so different. In fact, the rotations angles were so small that the controlled operations, which simulate the collisions, were very hard to be performed properly. In order to achieve the necessary precision in the experiment the rotations of θ had to be precisely adjusted for each value of η of the specific collision. For adjusting the angles values, two parameters may be varied, the amplitude and duration of the radio frequency pulses. However, varying these two parameters the sequence of operations needed for the corrections changes as well. Therefore, the correct pulse sequences were determined by combining the two analysis and testing in the spectrometer. A good precision could be achieved then and the small rotations, of the order of 0.30 degrees, could be implemented. For the state preparation the pulse sequence shown in Fig. 6 was performed, for more details see refs 36 and 37. The time τ2 of the free evolution here is related to the correlation parameter q as it is presented in Fig. 7. A the end of the circuit a magnetic field gradient in the z-direction is applied, which works as a transversal relaxation time killing the off-diagonal terms of the density matrix of system and environment. Finally, after each run, full state tomography was performed in the state of the system34.

View Article: PubMed Central - PubMed

ABSTRACT

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

No MeSH data available.