Limits...
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.


Related in: MedlinePlus

(a) The nuclear spins of the atoms of fluorine of the C2F3I molecule are the qubits. Two of them represent the environment and the other one is the system. Their interaction is showed in this pictorial representation of our collisional model. The action of the environment on the system’s qubit is represented by the two boxes and the demon. In the first collision, the demon will toss a coin and will decide if he will operate either  or  on the system ρ(0). Afterwards he can still decide if the operation done in the second collision is correlated or not with the previous one, resulting in the state ρ(2). (b) A quantum circuit that describes the experiment. The environment is prepared in state ρenv and will serve as the control qubit for the controlled operation that happen on the state of the system ρ. After that a quantum state tomography is performed on the first particle in order to determine the state of the system.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5037399&req=5

f1: (a) The nuclear spins of the atoms of fluorine of the C2F3I molecule are the qubits. Two of them represent the environment and the other one is the system. Their interaction is showed in this pictorial representation of our collisional model. The action of the environment on the system’s qubit is represented by the two boxes and the demon. In the first collision, the demon will toss a coin and will decide if he will operate either or on the system ρ(0). Afterwards he can still decide if the operation done in the second collision is correlated or not with the previous one, resulting in the state ρ(2). (b) A quantum circuit that describes the experiment. The environment is prepared in state ρenv and will serve as the control qubit for the controlled operation that happen on the state of the system ρ. After that a quantum state tomography is performed on the first particle in order to determine the state of the system.

Mentions: We encoded the system-environment state in a sample of trifluoroiodoethylene (C2F3I). The NMR experiment was performed using a 500 MHz Varian spectrometer with the used sample diluted (~1%) in deuterated acetone (containing 97% of deuterium). A single molecule of C2F3I contains three atoms of fluorine with nuclear spin-1/2, each of them representing a qubit. One of the atoms will be regarded as the system and the other two as the environment. These spins interact with each other and with applied magnetic fields as well. We designed the experiment to implement the operations represented in the quantum circuit of Fig. 1: the first qubit, top line in the circuit, represents the system and the other lines are the qubits of the environment. The two qubits of the environment are initially prepared in a correlated state where “0” means spin up and “1” means spin down. In each collision, the state of the system undergoes a random-walk type of evolution, changing conditionally to the environment: environmental spin up induces a rotation in a certain direction (say, x), whereas environmental spin down induces a rotation in the orthogonal direction (y). This situation can be summed up by the unitary transformation where /j〉〈j/ represents the internal state of an environmental particle and the exponentials dictate the system’s rotations.


High Resolution non-Markovianity in NMR
(a) The nuclear spins of the atoms of fluorine of the C2F3I molecule are the qubits. Two of them represent the environment and the other one is the system. Their interaction is showed in this pictorial representation of our collisional model. The action of the environment on the system’s qubit is represented by the two boxes and the demon. In the first collision, the demon will toss a coin and will decide if he will operate either  or  on the system ρ(0). Afterwards he can still decide if the operation done in the second collision is correlated or not with the previous one, resulting in the state ρ(2). (b) A quantum circuit that describes the experiment. The environment is prepared in state ρenv and will serve as the control qubit for the controlled operation that happen on the state of the system ρ. After that a quantum state tomography is performed on the first particle in order to determine the state of the system.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: (a) The nuclear spins of the atoms of fluorine of the C2F3I molecule are the qubits. Two of them represent the environment and the other one is the system. Their interaction is showed in this pictorial representation of our collisional model. The action of the environment on the system’s qubit is represented by the two boxes and the demon. In the first collision, the demon will toss a coin and will decide if he will operate either or on the system ρ(0). Afterwards he can still decide if the operation done in the second collision is correlated or not with the previous one, resulting in the state ρ(2). (b) A quantum circuit that describes the experiment. The environment is prepared in state ρenv and will serve as the control qubit for the controlled operation that happen on the state of the system ρ. After that a quantum state tomography is performed on the first particle in order to determine the state of the system.
Mentions: We encoded the system-environment state in a sample of trifluoroiodoethylene (C2F3I). The NMR experiment was performed using a 500 MHz Varian spectrometer with the used sample diluted (~1%) in deuterated acetone (containing 97% of deuterium). A single molecule of C2F3I contains three atoms of fluorine with nuclear spin-1/2, each of them representing a qubit. One of the atoms will be regarded as the system and the other two as the environment. These spins interact with each other and with applied magnetic fields as well. We designed the experiment to implement the operations represented in the quantum circuit of Fig. 1: the first qubit, top line in the circuit, represents the system and the other lines are the qubits of the environment. The two qubits of the environment are initially prepared in a correlated state where “0” means spin up and “1” means spin down. In each collision, the state of the system undergoes a random-walk type of evolution, changing conditionally to the environment: environmental spin up induces a rotation in a certain direction (say, x), whereas environmental spin down induces a rotation in the orthogonal direction (y). This situation can be summed up by the unitary transformation where /j〉〈j/ represents the internal state of an environmental particle and the exponentials dictate the system’s rotations.

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.


Related in: MedlinePlus