Limits...
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

The dynamics of a BEC’s position when the system is initialised in the state. Several values of the photon number, N, were used and dissipative effects were considered. The simulations were performed in units of Ω with g0 = 32.8Ω, κc = 0.17Ω and .
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4561959&req=5

f8: The dynamics of a BEC’s position when the system is initialised in the state. Several values of the photon number, N, were used and dissipative effects were considered. The simulations were performed in units of Ω with g0 = 32.8Ω, κc = 0.17Ω and .

Mentions: where the time dependence in the Hamiltonian describes the alternation between the two different opacity regimes, Eq. (6) and Eq. (8). Here the parameters κc and γM denote the cavity and mechanical damping rates respectively. Before continuing, it will be assumed that the mechanical damping rate, γM, is negligible with respect to the optical damping rate during the time scales that will be considered, 19. The above master equation was solved using MATLAB’s Quantum Optics Toolbox (QOT). The alternation between the reflective/transparent regimes can be simulated by performing successive simulations under each regime. We explored the accuracy of our numerics using various indicators. Both Tr and the traces of the reduced systems were unity to within the absolute and relative error (10−8), of the integrator in QOT. A more important source of numerical error arises from truncating the Hilbert spaces of the cavities and membranes. Analytically each of these are infinite dimensional but in the numerical simulation we truncate the individual cavity Hilbert spaces to n ≤ 4, while the membrane’s Hilbert space is truncated to n ≤ Ntrunc. The cavity Hilbert space truncation is found to be adequate while in Fig. 7 we plot the time dependence of the largest Fock element of the reduced density matrix of the membrane: . We must choose a Fock state truncation Ntrunc large enough to avoid significant population in this element during our simulation and we set Ntrunc = 40. By solving Eq. (27) with the initial condition the driving of the membrane’s displacement can be demonstrated, see Fig. 8. To examine the dependence of the photon number difference, Δ, on the maximal displacement, simulations were performed using several experimentally achievable values of N. A linear increase in the maximal displacement with N, predicted by Eq. (7), can be clearly observed in Fig. 8 where the mechanical frequency was set to kHz, the mechanical coupling rate to MHz, the cavity damping rate to kHz19, with a BEC of mass m = 17.3 ag18. The results also show that nanometre displacements of the BEC’s center of mass position from the origin can be attained with only three flips of the two cavity states. While the results show that under these conditions initialising the cavity modes in small number states is somewhat effective for displacing the BEC, many more flips are required to achieve large spatial displacements of more massive membranes. Under these conditions performing more than five flips is not possible if the cavities are initialised in small number states as, in this case, the cavity damping rate is on the order of the mechanical frequency (). This means that by the time the BEC reaches its maximal displacement a significant portion of the photons are lost from the cavity. The loss of photons from the cavity also produces a short time delay between the point in which the membrane achieves its maximal displacement and the application of the flip. This is most easily explained in the displaced harmonic oscillator picture, Fig. 2. As the system evolves photons are lost from the cavities causing the center of the two potential wells to shift towards the origin. This results in the achievement of maximal displacements at times slightly shorter than those predicted in Eq. (7). The times predicted by Eq. (7) were used in these simulations to demonstrate this effect as realistically these short time delays must be accounted for.


Deterministic Creation of Macroscopic Cat States.

Lombardo D, Twamley J - Sci Rep (2015)

The dynamics of a BEC’s position when the system is initialised in the state. Several values of the photon number, N, were used and dissipative effects were considered. The simulations were performed in units of Ω with g0 = 32.8Ω, κc = 0.17Ω and .
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f8: The dynamics of a BEC’s position when the system is initialised in the state. Several values of the photon number, N, were used and dissipative effects were considered. The simulations were performed in units of Ω with g0 = 32.8Ω, κc = 0.17Ω and .
Mentions: where the time dependence in the Hamiltonian describes the alternation between the two different opacity regimes, Eq. (6) and Eq. (8). Here the parameters κc and γM denote the cavity and mechanical damping rates respectively. Before continuing, it will be assumed that the mechanical damping rate, γM, is negligible with respect to the optical damping rate during the time scales that will be considered, 19. The above master equation was solved using MATLAB’s Quantum Optics Toolbox (QOT). The alternation between the reflective/transparent regimes can be simulated by performing successive simulations under each regime. We explored the accuracy of our numerics using various indicators. Both Tr and the traces of the reduced systems were unity to within the absolute and relative error (10−8), of the integrator in QOT. A more important source of numerical error arises from truncating the Hilbert spaces of the cavities and membranes. Analytically each of these are infinite dimensional but in the numerical simulation we truncate the individual cavity Hilbert spaces to n ≤ 4, while the membrane’s Hilbert space is truncated to n ≤ Ntrunc. The cavity Hilbert space truncation is found to be adequate while in Fig. 7 we plot the time dependence of the largest Fock element of the reduced density matrix of the membrane: . We must choose a Fock state truncation Ntrunc large enough to avoid significant population in this element during our simulation and we set Ntrunc = 40. By solving Eq. (27) with the initial condition the driving of the membrane’s displacement can be demonstrated, see Fig. 8. To examine the dependence of the photon number difference, Δ, on the maximal displacement, simulations were performed using several experimentally achievable values of N. A linear increase in the maximal displacement with N, predicted by Eq. (7), can be clearly observed in Fig. 8 where the mechanical frequency was set to kHz, the mechanical coupling rate to MHz, the cavity damping rate to kHz19, with a BEC of mass m = 17.3 ag18. The results also show that nanometre displacements of the BEC’s center of mass position from the origin can be attained with only three flips of the two cavity states. While the results show that under these conditions initialising the cavity modes in small number states is somewhat effective for displacing the BEC, many more flips are required to achieve large spatial displacements of more massive membranes. Under these conditions performing more than five flips is not possible if the cavities are initialised in small number states as, in this case, the cavity damping rate is on the order of the mechanical frequency (). This means that by the time the BEC reaches its maximal displacement a significant portion of the photons are lost from the cavity. The loss of photons from the cavity also produces a short time delay between the point in which the membrane achieves its maximal displacement and the application of the flip. This is most easily explained in the displaced harmonic oscillator picture, Fig. 2. As the system evolves photons are lost from the cavities causing the center of the two potential wells to shift towards the origin. This results in the achievement of maximal displacements at times slightly shorter than those predicted in Eq. (7). The times predicted by Eq. (7) were used in these simulations to demonstrate this effect as realistically these short time delays must be accounted for.

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