Idea Transcript
Using Quantum Coherence to Improve the Efficiency of Quantum Heat Engines Marlan Scully Texas A&M Universityy
Quantum Heat Engine Power Increased by Quantum Coherence Marlan Scully
with K. Chapin, . Chapin, K. K. Dorfman Dorfman, , B. B. Kim, Kim, and A. and A. Svidzinsky Svidzinsky
Texas A&M University and Texas A&M University and Princeton Princeton University University
Quantum Coherence Can Improve Q Quantum Heat Engine (QHE) Efficiency g (Q ) y I. Quantum Thermodynamics II. Photo-Carnot QHE III. The Laser as a QHE Q 1.
From Detailed Balance
2. Quantum Coherence Can Improve Laser QHE Quantum Efficiency by Breaking Detailed Balance Q IV. The Photocell as a QHE 1.
From Detailed Balance
2. Q Quantum Coherence Can Improve p Photocell Q QHE Q Quantum Efficiency y by Breaking Detailed Balance V.
Noise Induced Quantum Coherence Can Enhance: 1) Laser QHE Power 1). 2). Photocell QHE Power 3). Efficiency of Photosynthesis
Heat Engines • Classical Heat Engines produce useful work by extracting energy from a high temperature g gy g p energy source and rejecting entropy to a low temperature entropy sink. • A Photo‐Carnot Engine A Photo Carnot Engine is a Carnot cycle engine in is a Carnot cycle engine in which photons are the working fluid and the piston is driven by radiation pressure. Quantum coherence allows us to achieve thermodynamic efficiency beyond the Carnot limit without violating the second law. violating the second law. • Laser and Photocell Quantum Heat Engines are driven by thermal radiation and governed by the l laws of quantum thermodynamics. f h d i
Laser/Photocell Quantum Heat Engines Timeline i li • 1900 Planck Entropy of Thermal Light py g • 1905 Einstein Photon Concept, 1917 Stimulated Emission, Detailed Balance • 1954 Gordon, Zeiger, and Townes G d Z i dT Fi M First Maser • 1959 Maser as a Quantum Heat Engine • 1994 TAMU Lasing Without Inversion 1994 TAMU Lasing Without Inversion • 2003 Photo‐Carnot Quantum Heat Engine • 2010 Photocell Quantum Efficiency Improved by Q y p y Quantum Coherence • 2011 Laser and Photocell Quantum Heat Engines 5
Quantum Thermo I Planck studies Entropy of Light to Arrive at the Quantum* Wein Entropy
1 2S 2 b
where average energy of oscillator with frequency
Planck Entropy 1900
kB 2S 2 ( )
e / k BT 1
*Planck Photon Statistics and Bose Einstein condensation, Progress in Optics 2007
Quantum Thermo II Einstein studies Entropy of Light to Arrive at the Photon* Fluctuations E 2 2
n
2
wave
n particle
Wave Particle Duality 1905 Wave Particle Duality 1905
*Progress in Optics 2007
Quantum Coherence Can Improve Q Quantum Heat Engine (QHE) Efficiency g (Q ) y I. Quantum Thermodynamics II. Photo-Carnot QHE III. The Laser as a QHE Q 1.
From Detailed Balance
2. Quantum Coherence Can Improve Laser QHE Quantum Efficiency by Breaking Detailed Balance Q IV. The Photocell as a QHE 1.
From Detailed Balance
2. Q Quantum Coherence Can Improve p Photocell Q QHE Q Quantum Efficiency y by Breaking Detailed Balance V.
Noise Induced Quantum Coherence Can Enhance: 1) Laser QHE Power 1). 2). Photocell QHE Power 3). Efficiency of Photosynthesis
Photo‐Carnot Engine • Working Fluid(radiation) heated by two‐level atoms
Entropy Sink The image part with relationship ID rId5 was not found in the file.
M. Scully, M. Zubairy, G. Agarwal, and H. Walther y y g
10
Single Mode = Single Atom Single Mode Single Atom PV kT PV n kT
(O atom) (One t ) kT n ((One mode))
Tc c 1 Th
Rate equation for photon number (I) Rate equation for photon number (I)
12
Lasing Without Inversion
(a) Use of quantum coherence in ground state b,c to cancel absorption (b) the use quantum coherence in the excited state a,b a b to cancel emission
nlaser (n 1)( Aa 2 Bb 2 ) n Aa Bb
2
13
‘‘Continuous wave (cw) amplification and laser oscillation without population inversion have been observed…’’
14
Photo‐Carnot Photo Carnot Engine Engine • Working Fluid heated by phaseonium Working Fluid heated by phaseonium Entropy
The image part with relationship ID rId3 was not found in the file.
15
Rate equation for photon number (II)
16
Efficiency of a Quantum Carnot Engine Efficiency of a Quantum Carnot Engine
17
Quantum Coherence Can Improve Q Quantum Heat Engine (QHE) Efficiency g (Q ) y I. Quantum Thermodynamics II. Photo-Carnot QHE III. The Laser as a QHE Q 1.
From Detailed Balance
2. Quantum Coherence Can Improve Laser QHE Quantum Efficiency by Breaking Detailed Balance Q IV. The Photocell as a QHE 1.
From Detailed Balance
2. Q Quantum Coherence Can Improve p Photocell Q QHE Q Quantum Efficiency y by Breaking Detailed Balance V.
Noise Induced Quantum Coherence Can Enhance: 1) Laser QHE Power 1). 2). Photocell QHE Power 3). Efficiency of Photosynthesis
Quantum Heat Engine with and without Quantum Coherence ih d ih h
LLaser Q. H. E. Q H E Laser Q.H.E. by Scovil and Schulz‐DuBois Lasing without inversion Supercharged Quantum heat engine Supercharged Quantum heat engine
19
Laser Quantum Heat Engine (QHE)
Boltzmann distribution
At threshold (nb=na) efficiency of maser QHE
20
At threshold
21
Summary • Efficiency Efficiency from QHE can exceed the classical from QHE can exceed the classical Carnot Efficiency by using phased three‐level atoms. atoms • The Photo‐Carnot QHE can produce work from a single thermal bath from a single thermal bath. • Efficiency of Laser QHEs can be increased by quantum coherence. h
22
Quantum Coherence Can Improve Q Quantum Heat Engine (QHE) Efficiency g (Q ) y I. Quantum Thermodynamics II. Photo-Carnot QHE III. The Laser as a QHE Q 1.
From Detailed Balance
2. Quantum Coherence Can Improve Laser QHE Quantum Efficiency by Breaking Detailed Balance Q IV. The Photocell as a QHE 1.
From Detailed Balance
2. Q Quantum Coherence Can Improve p Photocell Q QHE Q Quantum Efficiency y by Breaking Detailed Balance V.
Noise Induced Quantum Coherence Can Enhance: 1) Laser QHE Power 1). 2). Photocell QHE Power 3). Efficiency of Photosynthesis
Photovoltaics Enhanced by Microwave Induced Quantum Coherence
Outline
Solar spectrum with the bandgaps of semiconductors Gregory F. Brown, and Junqiao Wu, Laser & Photon Review 3, No. 4, 394, (2009)
Quantum Dot Photo/Solar Cell Solar cell with array of quantum dots
Texas A&M Texas A&M University
Electron-hole separation
Dividing photon flux onto monochromatic components t
Solar Cells and Detailed Balance
P. Würfel, P Würfel Chimia 61, 61 770 (2007) “That leaves radiative recombination as the major [energy loss] process. Can this be avoided? The answer is no. If a radiative upward transition to generate the excitation is allowed, its reversal, the radiative downward transition must be allowed as well.”
Average photon number
Thermodynamic efficiency
Thermodynamic efficiency
Detailed balance revisited Detailed balance revisited “That That leaves radiative recombination as the major [energy loss] process. Can this be avoided? The
Yes!
answer is no. If a radiative upward transition to generate the excitation is allowed, its reversal, the radiative downward transition must be allowed as well well.”
can be mitigated by breaking detailed balance via quantum coherence! via quantum coherence!
Summary • Quantum coherence induced by an external microwave field can increase the quantum efficiency ( (open circuit voltage) of the photocell. i i l ) f h h ll • Furthermore Furthermore such a coherent driven photocell such a coherent driven photocell generates more power. The extra power produced by the device is much larger then that derived from the g microwave source which creates the coherence. • Induced coherence results in more efficient utilization of the pump photons by increasing absorption and/or quenching unwanted emission absorption and/or quenching unwanted emission.
Quantum Coherence Can Improve Q Quantum Heat Engine (QHE) Efficiency g (Q ) y I. Quantum Thermodynamics II. Photo-Carnot QHE III. The Laser as a QHE Q 1.
From Detailed Balance
2. Quantum Coherence Can Improve Laser QHE Quantum Efficiency by Breaking Detailed Balance Q IV. The Photocell as a QHE 1.
From Detailed Balance
2. Q Quantum Coherence Can Improve p Photocell Q QHE Q Quantum Efficiency y by Breaking Detailed Balance V.
Noise Induced Quantum Coherence Can Enhance: 1) Laser QHE Power 1). 2). Photocell QHE Power 3). Efficiency of Photosynthesis
Noise induced quantum coherence
External source: External source: Lasing Without Inversion Supercharged Quantum Heat Engine No external field Fano interference (quantum noise) Agarwal (Fano‐Harris) lasing without inversion (Fano Harris) lasing without inversion
“…The preceding coherent drive model illustrates the role of quantum coherence in a simple way. However, it is possible to generate coherence without the use of an external field. For example, quantum noise induced coherence via Fano coupling…”
Fano Interference I. LWI
Fano Interference II. Tunneling g
1 2 2 b
Bare state Bare state
2
a1 a2 b
Mixing of damping terms due to Fano
Noise induced coherence
Steady state coherence
Steady state coherence
Noise induced quantum coherence can double Noise induced quantum coherence can double the laser the laser power at no extra cost!
Entropy Sink
Energy Source
Tc
Th laser
laser h 1 TThc
a Th b
a
laser l
Tc
Plaser h nh nc laser
Th b1 b2
laser
Tc
Plaser 2 h nh nc laser
Noise induced coherence can double Noise induced coherence can double photocell power at photocell power at no extra cost! Transparent electrode
a
Quantum dots
a
Tc
b
Load
eVoc h 1 TThc
j
Th
n
j
Th
p
Tc
Tc
Pcell 12 e h nhV
b1 b2
Tc
Pcell e h nhV
For proper cell design noise-induced coherence is robust against g environmental decoherence 0.04
Cell p power
Full coherence
0.03
0.02
~
=10 =100~ No coherence
0.01
0.00 0.0
0.5
1.0
Energy
1.5
Robustness of noise induced coherence a 1
Ta , nc
2
~
c
TS , n
~1
b1
b2
12
j
v ~2 Ta , nv
i
Noise induced coherence:
Noise induced coherence in p photosynthetic systems y y
Konstantin Dorfman, Dmitri Voronine, Shaul Mukamel, and Marlan Scully
Charge separation in photosynthesis
Reaction Center of PSII of PSII Special pair
Photon echo experiments reveal quantum coherence in photosynthetic complexes
But: previous studies used lasers to induce quantum coherence. Can we get noise‐induced quantum coherence in photosynthetic complexes?
Conclusion: noise‐induced quantum coherence can enhance electron transport yield in photosynthetic complexes
SUMMARY Quantum Coherence Can Improve Quantum Heat Engine (QHE) Efficiency I. Quantum Thermodynamics II. Photo-Carnot QHE Q III. The Laser as a QHE 1.
From Detailed Balance
2. Quantum Coherence Can Improve Laser QHE Quantum Efficiency by Breaking Detailed Balance IV The Photocell as a QHE IV. 1.
From Detailed Balance
2. Quantum Coherence Can Improve Photocell QHE Quantum Efficiency Breaking Detailed Balance V.
Noise Induced Quantum Coherence Can Enhance: 1). Laser QHE Power 2). Photocell QHE Power 3). Efficiency of Photosynthesis
by
References 1. D.M. Greenberger, b N. Erez, M.O. Scully, ll A.A. Svidzinsky d k and d M.S. Zubairy. Progress in Optics, 50:275 (edited by E. Wolf, Elsevier, Amsterdam, 2007). 2 M.O. 2. M O Scully, S ll M.S. M S Zubairy, Z b i G.S. G S Agarwal, A l H. H Walther, W lth Science S i 299:862 (2003). 3. H.E.D. Scovil, E.O. Schulz‐DuBois, Phys. Rev. Lett. 2:262(1959). 4. M.O. Scully, Phys. Rev. Lett. 106:049801 (2011). 5. M.O. Scully, Phys. Rev. Lett. 104:207701 (2010). 6. M.O. Scully, y, K.R. Chapin, p , K.E. Dorfman,, M.B. Kim,, A.A. Svidzinsky, PNAS 108:15097 (2011). 7. K.E. Dorfman, D.V. Voronine, S. Mukamel, M.O. Scully, to be p published.
Laser QHE Entropy Sink
Energy Source
Tc
Th
laser laser
App I
a
laser
Th b
Tc
Laser power
MOS, Chapin, Dorfman, Kim, and Svidzinsky, PNAS 108 15097 (2011).
54
App II
Laser QHE with noise induced coherence Q Entropy py Sink
Energy gy Source
Tc
Th
a
laser
Th b1 b2
laser laser l
(
Tc
+