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Deterministic Creation of Macroscopic Cat States.

Lombardo D, Twamley J - Sci Rep (2015)

Bottom Line: Despite current technological advances, observing quantum mechanical effects outside of the nanoscopic realm is extremely challenging.In this work we develop a completely deterministic method of macroscopic quantum state creation.It is found that by using a Bose-Einstein condensate as a membrane high fidelity cat states with spatial separations of up to ∼300 nm can be achieved.

View Article: PubMed Central - PubMed

Affiliation: Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia.

ABSTRACT
Despite current technological advances, observing quantum mechanical effects outside of the nanoscopic realm is extremely challenging. For this reason, the observation of such effects on larger scale systems is currently one of the most attractive goals in quantum science. Many experimental protocols have been proposed for both the creation and observation of quantum states on macroscopic scales, in particular, in the field of optomechanics. The majority of these proposals, however, rely on performing measurements, making them probabilistic. In this work we develop a completely deterministic method of macroscopic quantum state creation. We study the prototypical optomechanical Membrane In The Middle model and show that by controlling the membrane's opacity, and through careful choice of the optical cavity initial state, we can deterministically create and grow the spatial extent of the membrane's position into a large cat state. It is found that by using a Bose-Einstein condensate as a membrane high fidelity cat states with spatial separations of up to ∼300 nm can be achieved.

No MeSH data available.


Related in: MedlinePlus

Classical visualisation of driving the membranes displacement by alternating the system between the two symmetrically displaced potential wells.The horizontal arrows represent the evolution of the membrane’s position in the high opacity regime where the membrane is reflective, , while the vertical arrows represent evolution in the transparent membrane regime, , or, the flipping of the cavity states. The sign  denotes the phase on the optomechanical driving term. Here the system is initialised in the state  with Δ > 0.
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f2: Classical visualisation of driving the membranes displacement by alternating the system between the two symmetrically displaced potential wells.The horizontal arrows represent the evolution of the membrane’s position in the high opacity regime where the membrane is reflective, , while the vertical arrows represent evolution in the transparent membrane regime, , or, the flipping of the cavity states. The sign denotes the phase on the optomechanical driving term. Here the system is initialised in the state with Δ > 0.

Mentions: where . This expectation value shows that if the state of the left and right cavity modes could be completely interchanged at times satisfying , the position of the membrane could be driven to even larger spatial extensions, see Fig. 2. The reason for this is that interchanging the state of the left and right modes effectively switches the phase on the interaction term in Eq. (6), that is, . This results in the membrane experiencing an extra displacement of after every photon number interchange. One way to interpret the effect of the phase on the optomechanical driving term is to consider the direction of the membranes displacement. For example, if the system is initialised in the state with Δ > 0 the phase on the optomechanical driving term is − and the membrane is displaced by in the positive x direction. Alternatively, if the system is initialised in the state the phase on the driving term will be + and thus the membrane will be displaced by the same amount, but in the opposite direction. An alternative explanation can be made in the displaced harmonic oscillator picture to easily visualise the protocol described to increase the membrane’s maximal displacement. The separate ± phases of the optomechanical driving term correspond to two separate quadratic potentials which are symmetrically displaced about the origin, as shown in Fig. 2. Carefully timing the optomechanical phase switching to occur when the membrane has reached a maximal displacement in one harmonic potential is analogous to shifting the membrane to the other, displaced, harmonic potential, where the potential energy is larger. If this process is repeated by switching the membrane between the two symmetrically displaced harmonic potentials its energy can sequentially be increased to achieve larger and larger spatial displacements, see Fig. 2. The interesting feature is that since the two harmonic potentials are identical the switching times are independent of the spatial extent of the membrane.


Deterministic Creation of Macroscopic Cat States.

Lombardo D, Twamley J - Sci Rep (2015)

Classical visualisation of driving the membranes displacement by alternating the system between the two symmetrically displaced potential wells.The horizontal arrows represent the evolution of the membrane’s position in the high opacity regime where the membrane is reflective, , while the vertical arrows represent evolution in the transparent membrane regime, , or, the flipping of the cavity states. The sign  denotes the phase on the optomechanical driving term. Here the system is initialised in the state  with Δ > 0.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4561959&req=5

f2: Classical visualisation of driving the membranes displacement by alternating the system between the two symmetrically displaced potential wells.The horizontal arrows represent the evolution of the membrane’s position in the high opacity regime where the membrane is reflective, , while the vertical arrows represent evolution in the transparent membrane regime, , or, the flipping of the cavity states. The sign denotes the phase on the optomechanical driving term. Here the system is initialised in the state with Δ > 0.
Mentions: where . This expectation value shows that if the state of the left and right cavity modes could be completely interchanged at times satisfying , the position of the membrane could be driven to even larger spatial extensions, see Fig. 2. The reason for this is that interchanging the state of the left and right modes effectively switches the phase on the interaction term in Eq. (6), that is, . This results in the membrane experiencing an extra displacement of after every photon number interchange. One way to interpret the effect of the phase on the optomechanical driving term is to consider the direction of the membranes displacement. For example, if the system is initialised in the state with Δ > 0 the phase on the optomechanical driving term is − and the membrane is displaced by in the positive x direction. Alternatively, if the system is initialised in the state the phase on the driving term will be + and thus the membrane will be displaced by the same amount, but in the opposite direction. An alternative explanation can be made in the displaced harmonic oscillator picture to easily visualise the protocol described to increase the membrane’s maximal displacement. The separate ± phases of the optomechanical driving term correspond to two separate quadratic potentials which are symmetrically displaced about the origin, as shown in Fig. 2. Carefully timing the optomechanical phase switching to occur when the membrane has reached a maximal displacement in one harmonic potential is analogous to shifting the membrane to the other, displaced, harmonic potential, where the potential energy is larger. If this process is repeated by switching the membrane between the two symmetrically displaced harmonic potentials its energy can sequentially be increased to achieve larger and larger spatial displacements, see Fig. 2. The interesting feature is that since the two harmonic potentials are identical the switching times are independent of the spatial extent of the membrane.

Bottom Line: Despite current technological advances, observing quantum mechanical effects outside of the nanoscopic realm is extremely challenging.In this work we develop a completely deterministic method of macroscopic quantum state creation.It is found that by using a Bose-Einstein condensate as a membrane high fidelity cat states with spatial separations of up to ∼300 nm can be achieved.

View Article: PubMed Central - PubMed

Affiliation: Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia.

ABSTRACT
Despite current technological advances, observing quantum mechanical effects outside of the nanoscopic realm is extremely challenging. For this reason, the observation of such effects on larger scale systems is currently one of the most attractive goals in quantum science. Many experimental protocols have been proposed for both the creation and observation of quantum states on macroscopic scales, in particular, in the field of optomechanics. The majority of these proposals, however, rely on performing measurements, making them probabilistic. In this work we develop a completely deterministic method of macroscopic quantum state creation. We study the prototypical optomechanical Membrane In The Middle model and show that by controlling the membrane's opacity, and through careful choice of the optical cavity initial state, we can deterministically create and grow the spatial extent of the membrane's position into a large cat state. It is found that by using a Bose-Einstein condensate as a membrane high fidelity cat states with spatial separations of up to ∼300 nm can be achieved.

No MeSH data available.


Related in: MedlinePlus